One of the more befuddling aspects of the Republican fight to stop Obamacare is the constant infighting within the GOP about how to go about blocking the health care law.

The party can't agree, because thwarting the implementation of Obamacare means different things depending on which GOP senator or representative you ask.

For the vocal faction of Republicans who helped Sen. Ted Cruz, of Texas, lead a 21-hour, filibuster-style speech this week against Obamacare, victory requires nothing short of stopping the entire law cold, even if it means blocking a resolution to keep the federal government from shutting down.

But for many other Republicans, success in repealing Obamacare can come piecemeal, by chipping away at parts of the law, like the 2.3-percent medical device tax that's unpopular with Democrats and Republicans, or a provision in the law that provides special healthcare subsidies for congressional staffers.

In the House, Speaker John Boehner, R-Ohio, lists on his website seven bills Congress has passed, which Obama signed into law, that reverse minor parts of the health care law.

"While our goal is to repeal all of Obamacare," the speaker's office touts, "we’ve already succeeded in repealing and defunding parts of it."

As Cruz pushed for the all-or-nothing approach on the Senate floor Tuesday and Wednesday, his more senior GOP colleagues outside the chamber called for a slower approach.

"There are portions of Obamacare that we absolutely could have focused attention on and I think would have gotten a lot of support," Sen. John McCain, R-Ariz., told the Washington Examiner in an interview following the Cruz filibuster.

One amendment Republicans are weighing would strike the medical device tax imposed under the law, which is supposed to raise $29 billion over the next decade but which both Republicans and Democrats have denounced as a job killer and an expense that will be passed along to consumers.

If the Senate held a vote on that amendment, McCain said, "We'd win."

Less likely, but possible, is an amendment that would eliminate special government subsidies for congressional staffers who will be forced to purchase health care insurance on the newly created exchanges.

Mike Tanner, a health care policy scholar at the libertarian Cato Institute, endorsed the "half-loaf" strategy, but only if the GOP pushes for something bigger than the repeal of the medical device tax, such as increasing the threshold for the employer mandate or raising the eligibility requirement for subsidies.

McCain argued that Senate Republicans "should try to focus amendments on specific provisions of Obamacare that most people object to."

McCain represents the majority of Senate Republicans, many of them veterans of the 1995 fight over federal government spending that resulted in a shutdown that turned politically disastrous for the GOP.

Sen. Orrin Hatch, R-Utah, who took office in 1977, remembers the 1995 shutdown well enough to know he doesn't care to repeat it.

Cruz's effort to try to block Obamacare through the 2014 government spending bill, Hatch acknowledged, has "rallied a lot of people out there who believe in what he's saying."

But the believers do not include the mainstream GOP.

"He feels deeply about it," Hatch said. "Some of us feel deeply the other way."

Sen. Susan Collins, R-Maine, arrived in the Senate in 1997, just as the GOP was trying to recover from the political fallout of the 1995 shutdown.

She views the difference between the Cruz camp's tactics on defunding the law and those of the rest of the GOP in practical terms.

Filibustering the government funding bill, Collins said, means there would be no one to write Social Security or Medicare checks, or to pay the military, for instance.

For now, Collins said, she is content to have the GOP "register our opposition," to the health care law by voting against a planned Democratic amendment that will strip out the defunding language. Collins acknowledged that the GOP has little chance of preventing the defunding language from being removed, but unlike Cruz, she's willing to support the final measure even though it will include money for the health care law, because it will keep the government running.

"I've been opposed to Obamacare since the beginning," Collins said. "I still am. But the whole frustration with (the Cruz filibuster), is that it doesn't accomplish the goal."

Sen. Jeff Sessions, R-Ala., is among the dozen Republicans who spoke on the Senate floor alongside Cruz during the filibuster. But Sessions doesn't support the total repeal approach, either. Parts of Obamacare should be retained, he said, such as the provision that prohibits insurance companies from rejecting people with pre-existing conditions and the rule allowing people to remain on their parents' health insurance policies until age 26.

"There are a lot of things that are popular in the bill that the majority of Republicans support," Sessions told the Examiner.

For Sessions, victory would mean a repeal of the individual mandate to purchase health insurance, a core part of the law.

Sessions said the Cruz filibuster, which lit up social media and the Capitol switchboards with praise for the Texas freshman from the GOP's conservative base, will help the party weaken the health care law even though it will not stop the law from being implemented on Oct. 1.

"In order to make fundamental changes in this law, you have to engage the American people," Sessions said. "What Cruz did was help generate the public interest and knowledge and tell people it's not hopeless, we can change the law."