WASHINGTON – Still sore after the whipping administered by President Obama and Senate Democrats over the government shutdown, congressional Republicans nonetheless insist they remain committed to shutting down the Affordable Care Act.

House Republicans, especially those with ties to the Tea Party, targeted what is popularly known as Obamacare from the outset of the raucous debate, refusing to support a temporary funding measure to carry the government beyond the federal fiscal year that began on Oct. 1 unless the healthcare law was defunded.

That effort famously went up in flames when lawmakers finally embraced a settlement that reopened the doors after a little more than two weeks without killing Obamacare. Now a question is plaguing a divided GOP caucus – how does the party accomplish the commonly held objective of bringing the ACA to a quick and bloody end since the Senate as presently composed would never go along? And, even if the upper chamber agreed, the president would issue a quick veto that could never gain the votes to be overturned.

In addition, Republicans must find some way to recover from the perception that the showdown over the shutdown was their Battle of the Bulge in the Obamacare fight – that last great shot at victory.

“This is our last chance and our last best chance to do something about this,” Sen. Marco Rubio (R-Fla.) said back in July.

But those long odds aren’t stopping congressional Republicans, particularly conservatives, from ramping up the fight. Some, like Sen. Ted Cruz (R-Texas), argue that the law’s bitter critics will do whatever it takes.

Cruz said he is “optimistic” about the ultimate death of Obamacare.

“I am inspired by the millions of Americans who have risen up,” he said. “And if the American people continue to rise up, I am confident that in time the U.S. Senate will follow the lead of the House of Representatives and listen to the American people. That is our job. That is our responsibility.”

A public revolt, he said, will “turn this around.”

“We’re going to restore jobs, we’re going to restore economic growth, we’re going to restore the ability of people struggling to climb the ladder and achieve the American dream and we’re going to stop the number-one job killer in this country that is Obamacare,” he promised.

Appearing a convention of the Texas Medical Association in Austin on Saturday, Cruz said the cause was lost because “Senate Republicans declined to unify and declined to support House Republicans” in repealing the law. He remains “hopeful that in the future the Senate will listen.”

Cruz has not ruled out navigating toward another governmental shutdown to push the issue when the current continuing resolution expires on Jan. 15. But apparently he will have to maneuver around Senate Republican Leader Mitch McConnell, of Kentucky, if he intends to do so.

Like Cruz, McConnell wants to kill Obamacare.

“This law is ravaging our economy, killing jobs, driving up premiums, and driving people off the health care plans they have and like, in droves,” McConnell said. “Its disastrous rollout is sign of even worse things to come. And the Democrat refusal to delay it reflects a stubborn ideological obsession that will do untold damage to our country. And Republicans remain determined to repeal this terrible law.”

But they will have to accomplish that, he said, without closing the government a second time. Appearing on Face the Nation on Sunday, McConnell said, “There will not be another government shutdown — you can count on that.”

“A number of us were saying back in July that this strategy could not and would not work,” McConnell said. “And of course it didn’t.”

McConnell acknowledged that Senate Republicans “have a math problem” when it comes to getting rid of Obamacare.

“It’s the following math problem — 55 Democrats and 45 Republicans,” he said. “We only control a portion of the government, and so that limits our ability to get rid of this horrible law.”

Sen. Lamar Alexander (R-Tenn.) concurs with McConnell, asserting that another government shutdown could prove disastrous.

“Every one of us has voted against Obamacare repeatedly,” Alexander said of Republicans. “Every one of us would vote to repeal it. But in my view the right tactic is not to shut down the government. It won’t work – Obamacare would just keep going and we would have shut down the government.”