It could come down to who blinks first.
Even if Republicans succeed beyond any current predictions and capture both the Senate and the House, they wouldn't have enough GOP votes to overcome President Barack Obama's veto.
But Republicans could still fall back on the congressional power of the purse, denying the administration billions of dollars to carry out the most far-reaching social legislation since Medicare and Medicaid.
"The endgame is a fight over funding," said Sen. Tom Coburn, R-Okla.
Faced with an opposition Congress "defunding" his health care plan, would Obama make a stand? Would he risk shutting down the Health and Human Services department, the IRS, or perhaps even the whole government?
"At that point, does he let everything else go?" asked former Rep. Tom Davis, a Virginia Republican elected in the GOP wave of 1994. "The game will be, does he shut the government down? Republicans can say, 'We gave him the money to fund other programs.'"
Davis, a moderate who watched former Speaker Newt Gingrich lose a confrontation with then-President Bill Clinton over a government shutdown, cautioned both sides: "The question is, do you win that argument or not?"
White House officials wouldn't comment.
Even if Republicans win, "they can beat their chests and say they won't fund the implementation of the law, but I think the law is the law, and if you can't change it, then, frankly, you have a responsibility to carry it out," Hoyer said. [See which industries are giving money to Hoyer's campaign.]
But months after Obama signed the legislation, extensive efforts by his administration to tout its benefits for seniors and families, small employers and large corporations, have failed to rally public opinion.
Major components such as taxpayer-subsidized coverage for millions now uninsured, an IRS-enforced mandate that most Americans carry a policy, and guaranteed coverage for people in poor health are still more than three years away.
That's a tantalizing opportunity for Republicans, and repealing "Obamacare" has become a campaign slogan in their drive to take the House. Some have proposed replacing the law with more modest alternatives.
"Repeal and replace" was the centerpiece this week on America Speaking Out, a website sponsored by the House GOP. They didn't mince words.
"Obamacare will have dire consequences for our nation," Rep. Steve King, R-Iowa, warned in a video on the site. "President Obama dismantled the finest medical system in the world and replaced it with a failed socialist model. The president nationalized your skin and everything inside it, and he enlarged the scope of the IRS by granting the agency the power to confiscate the assets of American who refuse to submit to the nanny state."
Nothing of the sort, say health care law backers. The law's requirement that most Americans carry insurance comes from a Republican proposal in the 1990s health care debate. Congress rejected a Medicare-like government option for all Americans that was the top priority for the political left. Most Americans will still have private insurance ten years from now.
Nonetheless, an advocacy arm of the Heritage Foundation, the prominent conservative think tank, is backing King's effort to force a floor vote on repeal soon.
Hoyer believes that's easier said than done. If Republicans win, "I think they would have second thoughts about repealing health care," the Democratic leader predicted.
Republicans would face tricky political and policy challenges, he explained, listing a few:
— Would they allow insurance companies to again deny coverage to children with medical problems? The new law prohibits that.