WASHINGTON – Senate Republicans are lining up to oppose the two-year budget agreement that passed the House on Thursday, placing the package in some jeopardy if it fails to attract the expected overwhelming Democratic support.

A growing number of GOP lawmakers who have expressed their reluctance, including Senate Republican Leader Mitch McConnell, of Kentucky, and Sen. John Cornyn, of Texas, the Senate Republican whip, are facing re-election challenges from their right flank, generating political pressure to oppose the plan.

In fact, Rep. Steve Stockman (R-Texas), who is running against Cornyn in the Texas Senate primary, opposed the package, calling it a “terrible budget deal” that “explodes the spending caps, balloons the deficit and betrays conservatives and the Constitution.”

Not to be outdone in a conservative state that views President Obama with a jaundiced eye, Cornyn told reporters during a conference call that he was concerned about the budget bill “because it breaks the spending caps that were a part of the Budget Control Act, which is one of the main reasons why federal spending has actually gone down this year and last year as opposed to having a straight upward trajectory.”

All three members of the Senate GOP leadership – McConnell, Cornyn and Sen. John Thune (R-S.D.), the caucus chairman – are expected to be no votes when Senate Democratic Leader Harry Reid, of Nevada, calls the measure up for a vote. Sen. Jeff Sessions (R-Ala.), ranking member on the Senate Budget Committee, is against it and anticipates Republicans will wage a filibuster, meaning proponents will be required to attract 60 votes in the 100-member chamber to gain passage.

Three lawmakers considered in the top tier of potential candidates for the Republican presidential nomination in 2016 – Sen. Ted Cruz (R-Texas), Sen. Marco Rubio (R-Fla.), and Sen. Rand Paul (R-Ky.) — have made it clear they intend to vote against the bill.

Reid hopes to hold a cloture vote on Tuesday, a procedural move that could lead to a final vote on the measure. But Sen. Dick Durbin, of Illinois, the Senate Democratic whip, told reporters on Thursday that leadership remains unsure they have the votes necessary to gain passage.

‘We need Republican votes to pass the budget agreement, period,” Durbin said. “We need at least five. And I’m hoping that there will be more than that.”

But at this early juncture, Durbin acknowledged, “there are not five Republicans who have announced they’re for it.”

At least two lawmakers who generally side with Democrats, Sen. Tom Harkin (D-Iowa) and Sen. Bernie Sanders (I-Vt.), are hinting they may oppose the bill, which could leave supporters needing seven Republican votes to pass. Sanders expressed disappointment that the budget package does nothing to create jobs and would not extend emergency unemployment benefits that expire at the end of this year for 1.3 million Americans.

“It is incomprehensible to me that the Republicans continue to protect huge corporate loopholes that benefit some of the largest and most profitable corporations in America,” Sanders said. “This obviously is not the budget I would have written.”

The two-year budget agreement, primarily the work of Sen. Patty Murray (D-Wash.), chairwoman of the Senate Budget Committee, and Rep. Paul Ryan (R-Wis.), chairman of the House Budget Committee, increases projected spending overall for the 2014 fiscal year from $967 billion to $1.012 trillion, with an additional increase to $1.014 trillion in 2015.

The agreement, which passed the House 332-94, would provide $63 billion in sequester relief over two years, split evenly between defense and non-defense programs. In fiscal year 2014, defense discretionary spending would be set at $520.5 billion and non-defense discretionary spending would be set at $491.8 billion. It replaces $63 billion in automatic spending cuts in part by reducing spending in some targeted programs while increasing revenues without benefit of a direct tax increase.