Conservatives instigating a confrontation with President Obama over his health care reforms don't necessarily believe the public would support the government shutdown that would inevitably ensue when the White House refuses to defund the Affordable Care Act.

But for many conservatives with Tea Party roots, waging the fight to scrap Obamacare -- or to achieve other legislative ends -- is just as important to winning and would demonstrate to voters their willingness to fight a high-stakes battle even if the odds are long and their own party leaders are questioning the political consequences of such a confrontation.

That schism over tactics, and a disagreement over electoral strategy in the 2014 mid-terms, highlight an on-going rift among Capitol Hill Republicans and help explain why a dozen GOP lawmakers are urging their party to threaten a politically risky government shutdown if Obama refuses to accept their plan to defund his landmark health care law.

"There will be no shutdown because [Senate Majority Leader Harry] Reid will find six votes and [House Speaker John] Boehner will capitulate. But fighting is the only thing that gives us a shot at 2014," said one congressional aide who works for a supporter of the defund-or-shutdown strategy. "The base already knows we're not going to win. What will disappoint them is if we don't fight."

Sen. John McCain, R-Ariz., who opposes the shutdown and defunding strategy, says that none of its proponents have made the case in private caucus meetings that the GOP can actually convince the public that defunding of Obamacare and the potential government shutdown are worthwhile. They also haven't laid out a plan showing how the GOP would deflect blame for the shutdown to Obama instead of congressional Republicans.

Advocates of the strategy have argued simply that it's the right thing to do. A second Republican senator who confirmed McCain's account but requested anonymity to discuss internal caucus deliberations, said supporters of the defund-or-shutdown strategy have been assured by outside conservative groups that the public would look favorably on the tactic if Republicans follow through.

"Our friends on the outside say it's winnable," is how proponents have described the strategy's political viability, this Republican senator said late Monday.

That doesn't mean the opposition to Obamacare isn't heartfelt -- or that Tea Party conservatives aren't attempting to block the law's implementation out of real fears for the damage they believe the statute will inflict on the economy and Americans' access to quality health care. In fact, this anxiety was a key consideration in their decision to risk squandering public dissatisfaction with Obamacare by employing a strategy to block it that has never proven politically successful, let alone sustainable.

Led by Republican Sens. Ted Cruz, of Texas; Mike Lee, of Utah; and Marco Rubio, of Fla.; and Republican Reps. Tom Graves, of Georgia; Mark Meadows of North Carolina; and Jim Jordan, of Ohio, a group of congressional Republicans are also urging their party not to support the continuing resolution needed to fund the government beyond the Sept. 30 end of the fiscal year unless Obama agrees to defund his health care reforms. Conservative activist groups have joined their clarion call.

Cruz sidestepped the question of whether Republicans could convince voters to blame Obama for any government shutdown, and indicated to reporters that public support for the strategy was crucial to its success. But he expressed confidence that the GOP could at least choke off funding for Obamacare and block further implementation if the party sticks together.

"If 41 Republicans stand together in the Senate or 218 Republicans stand together in the House, we can win this fight; we can defund Obamacare in its entirety," Cruz said. "But the only way that's going to happen is if the American people stand together and demand it."

"We've got 63 days," Cruz added.

However, some conservatives supporting the defund-or-shutdown strategy are also signaling a willingness to compromise on a spending bill that does not defund Obamacare -- as long as Republicans can negotiate acceptable concessions. Those concessions could include a further chipping away of Obamacare, a delay in the law's individual mandate, significant spending cuts or a combination of all three.

It's unclear how conservatives would explain to the Tea Party base why it was suddenly okay to drop their "last chance" to stop Obamacare before it goes into broad effect early next year. Backers of defund-or-shutdown also said that no one who truly opposes Obamacare would oppose their strategy.

But one conservative operative said compromise could be acceptable, depending on the circumstances.

"No one is going accept a pre-planned endgame because we don't know what is politically possible unless the GOP fights for every inch possible between now and Sept. 30," Heritage Action for America's Dan Holler said. "If they refuse to fight, some fig leaf delay won't be well received by the base."