Washington (CNN) -- It feels like a generation gap in the GOP.
Party elders appear increasingly concerned -- alarmed, even -- by an upstart effort by a new band of conservative lawmakers who want to shut down the federal government to protest the president's signature health care law, Obamacare.
The plan -- really more of a bargaining strategy -- was hatched primarily by lawmakers elected in the past few years -- exposing a rift in the GOP about how best to deal with the controversial health care law a year before the 2014 elections.
Supporters of a government shutdown are nowhere near critical mass even as 13 lawmakers recently signed a letter pledging opposition to any spending bill that doesn't defund the health law. To be successful, supporters of a government shutdown would need almost every Republican in the Senate to join their effort.
The GOP establishment is undoubtedly against a shutdown and many of them are becoming more vocal about it.
"The people of the nation would not be happy," said 2012 GOP presidential nominee Mitt Romney this week at a New Hampshire fundraiser about the possibility of a shutdown where Medicare benefits were skipped and troops didn't get paid.
"Most Americans are really tired of those kinds of shenanigans here in Washington," Arizona Sen. John McCain said on the conservative Michael Medved radio show last month.
A prominent conservative opinion maker, columnist Charles Krauthammer, called the idea "nuts."
Oklahoma Sen. Tom Coburn, who in the past has showed himself more than willing to step on the cogs of government if he disagrees with something, told the Washington Examiner a shutdown could cost Republicans control of the House. His Oklahoma colleague, Rep. Tom Cole, said on Fox News that shutting down the government would be like a legislative "temper tantrum."
But there is evidence that many in the outspoken party base would seriously disagree.
Tea party activists posted a video critical of freshman North Carolina Rep. Rob Pittenger, who drew jeers when he said during a town hall event in his district this week, "No," the party shouldn't shut the government down.
In an interview with CNN's Jim Acosta on Wednesday, Pittenger defended his decision to stand against tea party activists who called for a shutdown to defund Obamacare.
But Pittenger appears to be an exception as a younger lawmaker standing against shutdown proponents.
"The reality is, if we're willing to take a government shutdown unless we repeal Obamacare, ... we will lose that vote and Obamacare will survive it," Pittenger said. "Why would we go about a strategy that is doomed to failure."
Seeking to find middle ground in the party, a separate group of conservatives, including anti-tax activist Grover Norquist, have suggested instead to use the threat of shutdown to force a one year delay in implementing the law in place of pursuing a full repeal.
Backlash against Obamacare helped propel Republicans to take back control of the House in 2010. But exhaustive efforts since to repeal it have been ineffective.
Utah Sen. Mike Lee, the leader of the shutdown effort, was elected in 2010 after defeating longtime Republican Sen. Bob Bennett in the primary.
While his proposal to shut down the government is not embraced by establishment Republicans, it has drawn praise from Texas Sen. Ted Cruz and Florida Sen. Marco Rubio, two conservative stars who are believed to be considering runs for president in 2016.
Both also, like Lee, defeated more establishment GOP candidates on their way to Washington in 2010.
Senate Minority Leader Mitch McConnell, who hasn't taken a definitive position on the shutdown plan, is now facing a primary challenge in his bid for reelection in Kentucky.
Add to all of this the default, shutdown, economic calamity show that has been a Washington rerun due to a string of battles over the federal borrowing limit and government spending.
These conservative newcomers to Washington have seen the White House make dire warnings about how the recent forced spending cuts -- known formally as sequestration -- would have a negative effect on the government and military.
But months later, the forced spending cuts have been largely swept out of the news and the federal government -- from the Pentagon to the Health and Human Services Department -- has shown an ability to absorb it for now.
Cruz recently argued in a speech at the Heritage Foundation that shutting down the government wouldn't be that bad and could help the GOP.
"There are some Democrats, some in the media and some Republicans who portray a shutdown as a horrible calamity,"
Cruz said. "I think the term 'shutdown' is a misnomer. It's actually a partial, temporary shutdown. We have seen them before."
Cruz argued that Saturday and Sunday are kind of like government shutdowns.
But it is Romney, who has acknowledged that he's probably the last person Republicans are now looking to for advice, who gave the most earnest argument on Tuesday against shutting down the government.
"I badly want Obamacare to go away, and stripping it of funds has appeal. But we need to exercise great care about any talk of shutting down government," said Romney, according to a prepared text of his remarks at the private fundraiser. "What would come next ... what would come next when soldiers aren't paid, when seniors fear for their Medicare and Social Security, and when the FBI is off duty? I'm afraid that in the final analysis, Obamacare would get its funding, our party would suffer in the next elections, and the people of the nation would not be happy."
A spokesman for Cruz, responded to Romney on Wednesday, arguing that Americans see Obamacare as "train wreck."
"They expect their elected representatives to fight to undo it," said Cruz spokesman Sean Ruston. "If Republicans stand up for principle, we can win this debate."