WASHINGTON – Lawmakers with strong ties to the Tea Party movement have gained a toehold in the U.S. Senate but it appears they might have difficulty expanding their numbers this year.

Sen. Ted Cruz (R-Texas) and Sen. Rand Paul (R-Ky.) are among those associated with the conservative, grassroots drive that has proved influential within Republican Party politics in a relatively short period of time. But a review of upcoming Senate contests reveals that more establishmentarian Senate candidates maintain an edge – at least to this point – heading into the primary season.

Conservative disaffection for the manner in which mainstream Republicans are confronting President Obama and his policies, coupled with ongoing spending issues, have resulted in a higher than usual number of challenges to GOP incumbents.

Yet, in the first showdown of the primary season, establishment Republicans won hands down, with Senate Republican Whip John Cornyn, of Texas, blasting Rep. Steven Stockman (R-Texas) by more than 40 points. Cornyn is overwhelmingly favored to win a third term in the fall.

“I think we are going to crush them everywhere,” said Senate Republican Leader Mitch McConnell of Kentucky, who faces his own Tea Party challenge this year from Louisville businessman Matt Bevin. “I don’t think they are going to have a single nominee anywhere in the country.”

Tea Party supporters were heartened by the results in 2010 when incumbent Republican senator Bob Bennett, of Utah, lost to movement favorite Sen. Mike Lee (R-Utah) at the state’s GOP convention and when Sen. Lisa Murkowski (R-Alaska) lost the Republican primary to Joe Miller, although Murkowski recaptured her seat in a write-in campaign.

The Tea Party tasted success – though short-lived — again in 2012 when Indiana State Treasurer Richard Mourdock defeated Sen. Richard Lugar (R-Ind.), who was seeking a seventh term, in the GOP primary. Mourdock lost to Sen. Joe Donnelly, (D-Ind.) in the general election.

Despite some successful challenges, almost 99 percent of congressional incumbents won their primaries in 2012. History shows that since 1946 only five percent of such challenges have result in the office-holder losing his or her party’s nomination. This year 28 incumbents – 12 Republicans — are seeking reelection in the 36 Senate seats up for grabs. If the past is any guide, only one incumbent can expect to lose his or her re-nomination fight.

Of the 12 Republicans seeking re-election, seven – not counting Cornyn – are facing primary challenges. Polls show the incumbents, in most cases, maintaining substantial leads.

McConnell, who has weathered strong Tea Party criticism despite winning the endorsement of Paul, maintains a healthy lead over Bevin. A survey conducted Feb. 24-26 by Public Opinion Strategies shows McConnell gaining support over the past few months, leading Bevin 61 percent to 23 percent.

Regardless, Bevin is confident he can close the gap.

“I like where we are,” Bevin said at a recent forum sponsored by FreedomWorks. “It’s always good to be the underdog. It’s good to be the stealth player under the radar screen.”

The same situation can be found in Tennessee where Tea Party activists hoped to pick off Sen. Lamar Alexander (R-Tenn.). State Rep. Joe Carr mounted a challenge with the support of groups like Tea Party Nation and The Coalition for a Constitutional Senate.

While there has not been much polling in the race it appears Alexander maintains a large lead. A survey by North Star Opinion Research conducted Feb. 3-6 gave the incumbent a 45-point lead – 62 percent to 17 percent.

In Kansas, one of the nation’s most conservative states, activists continue to search for a way to dump GOP Sen. Pat Roberts, even though Heritage Action determined that he is the most conservative senator seeking re-election this cycle and is considered the upper chamber’s fourth most conservative member.

It appeared Roberts could face problems when it was revealed that he no longer actually resided in the state. A challenge was offered by Milton Wolf, a radiologist, political commentator and, interestingly, President Obama’s second cousin, making his first run for public office with the support of the Tea Party Express and the Senate Conservative Fund.

Again, polling is scarce but Public Policy Polling, an organization with Democratic ties, found Roberts ahead in a survey conducted Feb. 18-20 by 26 points – 49 percent to 23 percent. Wolf found some good news in the results – the incumbent remains below the magic 50 percent mark. The bad news is the survey found Kansas voters desire an even more conservative candidate than they appear to be getting and there is speculation that former congressman Todd Tiahrt might jump in.

To this point, Wolf retains strong Tea Party support.

“Unlike the career politicians that have buried future generations under crippling debt, Milton Wolf is a conservative game-changer that will tackle the complacency culture of D.C.,” said Amy Kremer, chairwoman of the Tea Party Express. “Dr. Milton Wolf has intimate knowledge of America’s healthcare system and is the perfect person to tackle President Obama’s failed healthcare policy.”

Wolf has offered an alternative to the “Obamacare train wreck,” Kremer said, displaying “that kind of conservative leadership that has been largely absent for far too long in D.C. I am confident Dr. Wolf will join the ranks of Senators Ted Cruz, Mike Lee, and Rand Paul when he is elected.”

The Tea Party faces better odds in two other races.

Many political observers, including the Cook Political Report, believe conservative activists have the best opportunity for a pick-up in Mississippi, where Sen. Thad Cochran, seeking a seventh six-year term, is facing a tough re-election fight against state Sen. Chris McDonald, who is drawing support from, among other groups, the Club for Growth and the Senate Conservatives Fund.

A recent poll by NSON Opinion Strategy, sponsored by the Tea Party Express, showed Cochran ahead 45 percent to 37 percent but McDaniel appears to be picking up steam. After being told McDaniel has support from Tea Party groups, the challenger slipped ahead, 42 percent to 41 percent.

“The battle lines are clearly drawn in this race,” said Matt Kibbe, president of FreedomWorks for America. “This is Cochran and his band of super lobbyists versus Chris McDaniel and the people of Mississippi.”

Kibbe criticized Cochran for 19 votes to raise the debt ceiling resulting in “over $10 trillion in debt, all to be passed on to children and grandchildren. It’s time for a new generation of representation that cares about families and small businesses in Mississippi.”

In South Carolina, Sen. Lindsey Graham, who has served as a Tea Party punching bag for months, faces six fellow Republicans who want to take his seat.

By all reports Graham maintains a healthy lead over the pack. A Winthrop University poll shows him with support from 45 percent of those questioned. The closest challenger is State Sen. Lee Bright, who has the endorsement of the Republican Liberty Caucus and a couple local Tea Party organizations, has support from a mere nine percent. Sabato’s Crystal Ball, a product of the University of Virginia Center for Politics, maintains that the race leans toward Graham.

The reason for some optimism among Tea Party activists is that Graham has to attract 50 percent of the vote in the June 10 primary or face a run-off against the second place finisher. If the other camps coalesce behind the surviving challenger, Graham could ultimately find himself involved in a tight contest.

Regardless, the Tea Party won’t leave the campaign season empty handed. Three incumbents who don’t face primary challenges – Sen. Jeff Sessions (R-Ala.), Sen. Jim Inhofe (R-Okla.), and Sen. Jim Risch (R-Idaho) – attract movement support and are odds-on favorites to win re-election in November. Sen. Tim Scott (R-S.C.), appointed to his seat after Jim DeMint resigned the seat to assume the leadership of the Heritage Foundation, is solidly in the Tea Party corner and faces nominal opposition.

And there are Tea Party candidates running for seats being vacated by Republicans who chose not to seek re-election. In Georgia, where Sen. Saxby Chambliss is stepping aside, five hopefuls are vying, each one endeavoring to out-conservative the other to gain movement support.

Rep. Paul Broun (R-Ga.) appears to have generated the most enthusiasm among Tea Party supporters – he carries the support of the Madison Project – but he is running tied for second, according to a poll conducted by Landmark/Rosetta Stone. The current leader is businessman David Perdue, with 21 percent, followed by Rep. Jack Kingston and Broun with 15 percent apiece.

Nebraska offers another opportunity, and confusion. In the race to replace the retiring Sen. Mike Johanns, Freedomworks originally endorsed former state treasurer Shane Osborn. But the organization changed its mind and now is getting behind Midland University President Ben Sasse, who has received support from various other Tea Party groups.

Kibbe explained his organization changed horses once Osborn aligned himself with Republican establishmentarians.

“At this point, it is clear that Shane Osborn formed allegiances with Mitch McConnell and the K Street lobbying class,” Kibbe said. “For us, that progression away from the grassroots has tipped the balance.”

Regardless, the most recent polls show Osborn leading Sasse 35 percent to 24 percent in a crowded field.

In Oklahoma, in a race to replace Sen. Tom Coburn, who announced his resignation at the end of this year, T.W. Shannon, the former speaker of the Oklahoma House of Representatives, has drawn the support of the Senate Conservatives Fund and Tea Party heavy-hitters like Sen. Lee. But the latest poll from Public Opinion Strategies, conducted March 16-17, shows him trailing Rep. James Lankford 37 percent to 28 percent.

And of course there are opportunities for Republicans – Tea Party or otherwise – to pick up seats currently held by Democrats.  But there again it appears GOP candidates with establishment ties hold an advantage over those with Tea Party support. In North Carolina, for instance, Greg Brannon, a doctor and Tea Party activist, trails state Rep. Thom Tillis, the speaker of the North Carolina House of Representatives, 23 percent to 15 percent in a Survey USA poll conducted March 27-31. The winner in that race will go on to face vulnerable Sen. Kay Hagan (D-N.C.) in the fall.