Washington (CNN) -- Right now, some Republican lawmakers in Washington may be wondering how to wiggle out from between a rock and a hard place.

On one hand, they're staring at a possible financial nightmare if the nation's debt limit isn't raised. On the other, many are feeling the heat from tea party demands that bluntly warn: Vote against us and suffer political consequences.

To be sure, Democrats are also under pressure from progressive constituencies who are pushing for more revenue in the form of tax increases -- and for them to stand firm against cuts to entitlements such as Social Security, Medicare and Medicaid.

But over its 2½-year existence, the tea party movement has placed its banner of less government spending at the center of the national conversation. So many activists are watching who's voting on what, even their conservative supporters in Congress -- and especially putting the squeeze on moderate Republicans.

What they're saying around the country is, "Do not raise the debt ceiling. It's that simple. It's time for Congress to get its fiscal house in order," Tea Party Patriots co-founder Jenny Beth Martin told CNN. The group is the nation's largest tea party organization.

Martin explained that her group's supporters want a balanced-budget amendment, significant spending cuts and lower taxes. And they don't want the debt limit raised.

This week, Tea Party Patriots' members and supporters are intensely calling various lawmakers: establishment Republicans, so-called "Blue Dog" Democrats and those freshmen Republicans elected to the House with tea party support.

"I think that it's accurate to call it pressure," Martin said. "The other thing is, we're holding these ... freshmen accountable. A lot of these freshmen ran on the promise that they were not going to increase the debt ceiling. Now, they're in D.C. with all of their colleagues on the Hill. And they're buying into the company line, forgetting about the fact that the American people have elected them not to do that."

For those who vote to raise the debt limit, "The American people are going to watch what they did, watch what happens to the economy and next November, I think there will be consequences," Martin said.

Another major tea party booster echoed the sentiment.

Brendan Steinhauser, director of federal and state campaigns for the Washington-based FreedomWorks, explained that he and other activists understand the possible financial implications if the debt limit is not raised.

"I think if you don't get significant cuts, you don't get a balanced-budget amendment as part of it, and you're raising taxes -- I just think that it's, politically, ... you'll definitely face serious challenges for your re-election," Steinhauser said.

He added: "Especially if you're a Republican. The tea party is going to be looking for a handful of examples to be made."

Rep. Steve Pearce, a freshman who won in New Mexico's 2nd Congressional District with tea party help, is one of 60 members of the House Tea Party Caucus.

In an interview with CNN, Pearce said he supports tea party ideals of less spending. And yet he still receives urgings from tea party supporters.

"We get e-mails frequently saying, 'Just hold the line, don't increase spending,' " Pearce said. "Many are saying, 'Don't vote for any debt ceiling.' But they also kind of qualify it by saying, if you could get a balanced budget amendment or get something significant in exchange -- they would understand it."

Does Pearce feel it amounts to tea party pressure?

"I don't think it's pressure. I think it's accountability," the congressman said.

Rep. Bill Cassidy, who represents Louisiana's 6th Congressional District, is also a member of the House Tea Party Caucus.

He too advocates for cuts in spending and is against tax increases. Cassidy is also getting phone calls and e-mails urging him not to budge.

"I have no doubt that there will be people disappointed with me however I vote on this, one way or the other," Cassidy said. "I'd like to think that what people are looking for is: Are you staying true to the principles that you ran on, which I hope to do and plan to do."

Meanwhile, those Republicans that tea party activists deem as moderate are also being watched.

For example, conservative activists recently targeted Sens. Orrin Hatch of Utah and Olympia Snowe of Maine by saying that both are less than conservative.

Steinhauser said that Hatch "has been voting with FreedomWorks ... quite strikingly in the last couple of years, every since tea party activists in Utah dethroned (former U.S. Sen.) Bob Bennett and replaced him with (Sen.) Mike Lee."

As for the senator from Maine, Steinhauser said: "I know that even Snowe is starting to sound like us, make certain phone calls to try to talk about how she's doing all these great things."

But Steinhauser continued, "I don't think they're really fooling anyone on what their overall record is."

A CNN analysis shows that Hatch always voted against raising the debt ceiling during President Barack Obama's time in office. The senator nearly always voted to raise the debt ceiling during President George W. Bush's administration -- the lone exception in the summer of 2008.

As for Snowe, she twice opposed a debt-limit increase and once supported it since during Obama's term. And the Maine Republican always voted to raise the debt ceiling under Bush.

Staffers for both senators defend their conservative bona fides and battle against tea party claims.

Ken Lundberg, Snowe's communications director, said the senator has voted against a debt-limit increase seven times with a Democrat in the White House and five times against with Republican presidents.

"This is not an issue where she's drawn a party line," Lundberg said, adding that Snowe has consistently acted on fiscal mechanisms to bring the deficit back in order and has long advocated a balanced-budget amendment.

A Hatch spokeswoman was far more blunt.

Antonia Ferrier, communications director in the Utah Republican's Senate office, defended Hatch's record -- and attacked tea party slams against it.

On the current debt ceiling negotiation, Ferrier said Hatch is a staunch supporter, and signer of, the "Cut, Cap, Balance" pledge, which demands no raising of the debt limit unless deep budget cuts, spending caps and a balanced-budget amendment come with it.

On Hatch's past debt ceiling votes, Ferrier said: "When you have a Republican president, historically what has happened is that the party of the president (and) the party in the majority in Congress have done that."

"It means nothing," she said.

And Ferrier reserved her fiercest fire for tea party claims -- specifically Steinhauser's assertion that Hatch has become more conservative only recently.

"Well, that's a very interesting quote from FreedomWorks considering that Dick Armey, the chairman of FreedomWorks, has also voted to raise the debt ceiling," Ferrier said. Armey is a former House majority leader.

Ferrier said that Armey "has actually been a lobbyist for a client who was trying to get stimulus money. He was also a lobbyist for an overseas bank trying to get a bailout. So FreedomWorks is not exactly operating as an honest broker."

"They are cherry-picking votes when Orrin Hatch may have voted with a whole bunch of other Republicans and saying that he is the only one. It's salacious, it's lies and they know it."

Steinhauser responded, accusing Hatch of "35 years of bad votes." He added: "This election is about Orrin Hatch and whether he deserves to be re-elected. It's nothing to do about Dick Armey or anybody else, current or former politician."

As for Armey's past work, Steinhauser said, "As chairman of FreedomWorks he hasn't done anything like that for us."

Steinhauser said the firm where Armey formerly worked lobbied on behalf of Democratic and Republican issues -- and that "Armey did work on Republican issues."