The Republican leadership has already given in to Tea Party demands. Under pressure from freshman members of Congress who said Republicans' original budget proposal fell short of their campaign promise, the House leadership slashed another $26 billion from their original draft, bringing the total reduction to $100 billion, closer to the campaign pledge in 2010.
The pressure from the Tea Party poses a unique challenge for the Republican leadership.
On the one hand, they have to heed the demands of Tea Party-supporting freshman lawmakers who insist they came to Washington on a mandate to cut spending and rein in the deficit. On the other hand, such pressure could pose a challenge in negotiating with Democrats and President Obama, who has already threatened to veto the continuing resolution passed by the House that would fund the government until October.
"We came into Congress with a mandate from the people that we represent and I think the cross section of America, everybody is saying we have a spending problem," said Rich Nugent, R-Fla., a freshman congressman who has called for deeper cuts than what Republicans initially proposed.
"America has a spending problem. Until we get that under control, America's at risk. I hear that consistently from people, whether they're Republicans or Democrats," he added. "We have got to get our house in order. We have got to cut spending."
The Tea Party has already cemented its role in state politics. In Florida, newly minted Gov. Rick Scott met with the movement's local leaders early last month to roll out his budget plan.
Wisconsin Gov. Scott Walker, whose campaign was heavily bankrolled by Tea Party groups and their supporters, is embroiled in a bitter battle with unions and state workers. The impasse has virtually shut down the state government but neither Walker nor conservatives are budging in their demands that unions' rights be curbed.
A federal government shutdown, however, is a different story. The partial government shutdown of 1996 was hugely unpopular, with Republicans taking most of the blame. A new Washington Post poll found that Americans would find both parties equally culpable if the government were to shutter.
And while rhetoric is easy, many people argue that Americans, for the most part, don't want the kind of cuts that Republicans are proposing, especially if it affects their own well-being and daily lives.
The GOP's proposed spending cuts would be a drag on the economy and slash economic growth by about 2 percent of Gross Domestic Product, according to a confidential report prepared by Goldman Sachs for its clients.
But Tea Party leaders are vowing to hold lawmakers accountable. They warn that the consequences for Republicans could be worse if they don't heed their demands.
"I think Republicans need to sort of own the courage of their convictions," Kibbe of FreedomWorks said. "I think there is a price to be paid politically for not being bold. You have this massive community of Tea Partiers, primarily independents, who are interested in policy, not political affiliation."