A growing chorus of conservative Republicans say the current fight over how to reopen the government has little to do with President Obama's healthcare law, raising new questions about what the GOP wants to end the current fiscal standstill.

Republican officials have insisted for days that they just want a chance to negotiate with Obama and Senate Democrats, in an effort to find a solution that’s currently nowhere in sight.

But with polls showing the GOP bearing the brunt of the blame for the current shutdown, fewer Republicans are demanding that changes to ObamaCare be part of any deal. Some Tea Party-backed lawmakers are even saying that the now five-day old shutdown could actually hurt Republicans chances to roll back the law.

Rep. Dennis Ross (R-Fla.), one of the dozens of House Republicans elected in the wave of 2010, said Saturday that the GOP’s only real chance to get their way on the healthcare law is at the ballot box in 2014.

“If we were just focused on the implementation, the American public would see just how bad it is,” Ross told reporters, pointing to glitches with ObamaCare’s launch this week.

“This is a gift that keeps on giving to the Republican Party if we let it. I mean, it did a wonderful thing for us in elections in 2010. It will do a phenomenal thing for us in the elections in 2014.”

Even Rep. Michele BachmannMichele Marie BachmannYes, condemn Roseanne, but ignoring others is true hypocrisy Bachmann won't run for Franken's Senate seat because she did not hear a 'call from God' Billboard from ‘God’ tells Michele Bachmann not to run for Senate MORE (R-Minn.), one of the most vocal GOP opponents of the healthcare law, said the fight had moved beyond ObamaCare as well. Asked Friday if the shutdown fight is still about the president's signature healthcare law, the Tea Party-favorite was clear.

"No," she said. "This is about opening up the federal government and making it work for the American people. That’s what we’re trying to do, is to get him [Obama] to resolve it.

"We don’t get the president," she added. "We want him to come over, talk to us. The doors are wide open, we’ve given him bill after bill after bill. At some point the president has to start talking.”

At the same time, House Republicans continue to push to open certain slivers of the government – even parts they have traditionally found overpriced or in need of reform.

Washington also has less than two weeks to raise the $16.7 trillion debt limit – a short window that's increasingly raising the likelihood that the two debates will merge. Those combined deadlines have Speaker John BoehnerJohn Andrew BoehnerFormer top Treasury official to head private equity group GOP strategist Steve Schmidt denounces party, will vote for Democrats Zeal, this time from the center MORE (R-Ohio) quietly feeling out the GOP conference on a potential broad fiscal deal.

BoehnerJohn Andrew BoehnerFormer top Treasury official to head private equity group GOP strategist Steve Schmidt denounces party, will vote for Democrats Zeal, this time from the center MORE and other GOP leaders had initially rejected the strategy of conditioning new spending on ObamaCare language, hoping to delay the battle for the debt ceiling debate.

They were forced to pull their bill, however, in the face of entrenched opposition from House conservatives who agree with Sen. Ted CruzRafael (Ted) Edward CruzSenate left in limbo by Trump tweets, House delays The Hill's Morning Report — Sponsored by PhRMA — Immigration drama grips Washington Senate Gang of Four to meet next week on immigration MORE (R-Texas), the loudest advocate for drawing a line in the sand on government funding.

Now, the Republican rank-and-file – and even some lawmakers close to Boehner – say they’re still not exactly sure what their offer will or should be to end the current gridlock.

Ross, for instance, said that pride had become a major reason for the deadlock, and noted that the current shutdown actually has little impact on funding for ObamaCare’s implementation.

Meanwhile, Rep. Marlin Stutzman (R-Ind.) was forced to backtrack this week after saying he didn’t know what the GOP wanted, and that lawmakers in the party had felt disrespected by Democrats and the president.

And other Republicans, like Rep. Doug Lamborn (R-Colo.), say they’re resigned to falling short in their efforts against ObamaCare, at least when it comes to the fight over government funding.

Lamborn told reporters Saturday that he "recognizes the writing on the wall," and that the effort to either defund or delay ObamaCare has "not been successful."

Rep. Blake FarentholdRandolph (Blake) Blake FarentholdSenators introduce bill to overhaul sexual harassment policy Freedom Caucus bruised but unbowed in GOP primary fights Five races to watch in the Texas runoffs MORE (R-Texas), another member of the 2010 class swept into office by ObamaCare, called the law “a big, shiny apple” that Republicans definitely viewed as the biggest job killer of all.

“But it’s certainly not the only one. And if we can make the same or bigger difference doing something other than ObamaCare, I don’t see why we wouldn’t do it,” Farenthold said, referencing potential change to entitlements, regulations and the tax code.

“The ObamaCare battle, I think, will live to be fought another day,” the Texas Republican added. “Because I think it will collapse under its own weight.”

Boehner has long sought a broad fiscal deal that would overhaul those areas, famously falling short in negotiations with Obama in 2011.

The Speaker and his allies are now talking up a potentially smaller deal, or a down payment on a bigger plan, that could include instructions for tax reform and some entitlement changes that the White House has supported in the past – like the “chained” consumer price index and means testing for Medicare beneficiaries.

Not that all conservatives have abandoned the ObamaCare-delay push as part of the current spending fight. Indeed, a number of Republicans said Saturday that the healthcare fight very much remains the underlying reason that the government remains shuttered.

"Absolutely," said Rep. Richard Hudson (R-N.C.). "That's the big issue."

Rep. John FlemingJohn Calvin FlemingCoast Guard suspends search for missing Ohio plane Freedom Caucus member to bring up bill on impeaching IRS chief GOP seeks to make it 52 MORE (R-La.) echoed that message. He acknowledged the the healthcare issue has disappeared amid the GOP's new piecemeal approach to the CR, but he was quick to add that the CR debate is "rapidly merging into the debt ceiling discussion," where Republicans will redouble their earlier efforts to prevent ObamaCare from taking full effect.

"It's still there,” Fleming said. “Healthcare will come back up again."

"You've seen the long laundry list of things we want to discuss and debate," he added, "everything from Keystone XL to coal ash to the REINS Act, and again revisit the one-year delay of ObamaCare."

But for conservatives like Ross, the current fight also overshadows the strides that Republicans have made in restraining government spending – another key plank that the class of 2010 ran on.

Democrats, for instance, are willing to reluctantly support a short-term bill that funds the government at the $986 billion sequester-level level – a figure far below what most in the party prefer.

And, Ross said, Republicans had found a way to bottle up government spending like no Congress had since the Korean War-era.

“That’s significant,” Ross said. “If we could have said we were going to do that three years ago when we were elected, people wouldn’t have believed us.”

Vicki Needham and Talia Mindich contributed.