Washington (CNN) -- House Republicans called off a vote Thursday on Speaker John Boehner's plan that would raise the nation's debt ceiling and enact sweeping cuts in government spending, but the possibility remained that the measure could come up on Friday.

"Members are advised that there will be NO VOTES in the House tonight," said a message from House Majority Whip Kevin McCarthy's office. "We apologize for the late notice."

The delay in voting on the proposal revealed a deep rift within the GOP that could undermine the party's latest attempt to avoid an unprecedented national default and stave off potential economic catastrophe.

Boehner, R-Ohio, was unable to muster sufficient support from his own caucus to guarantee his proposal would pass in the face of expected unified Democratic opposition. Even if the Boehner plan does pass the House, Senate Majority Leader Harry Reid, D-Nevada, has promised the Democratic-controlled Senate will block it.

McCarthy's announcement came more than four hours after the House had been expected to vote on the Boehner plan. The House Republican caucus then announced a previously unscheduled meeting for 10 a.m. Friday morning.

In an indication of the seriousness of the debt ceiling issue in Congress, Reid also announced that Senate Democrats will hold their own meeting at the same time.

Democratic leader Rep. Nancy Pelosi accused the Republicans of taking the country to "the brink of economic chaos," saying they needed to come back to "the table to negotiate a bipartisan, balanced agreement."

The tone was similar from Democratic National Committee Chair Debbie Wasserman Schultz, who said Thursday's developments should be a "wakeup "call to the "intransigent Republican majority" in the House.

"Now that his attempt at partisan politicking has failed, I hope that Speaker Boehner will finally join with President Obama and Democratic Congressional leaders in a serious way to enact bipartisan legislation to prevent an historic and catastrophic default on the United States' debt," she said.

Earlier, Rep. Nan Hayworth, R-New York, who supports the Boehner plan, told CNN that some members "have had a lot of deep thinking to do" about their votes, and said the delay might be to confirm "the last few" supporting votes.

The vote in the House had been scheduled for roughly 6 p.m. ET. Few if any Democrats were expected to back the measure. Assuming House Democrats remain united against the bill, Boehner will need the support of at least 216 of the House's 240 Republicans.

After announcement of the delay in the vote, conservative congressmen were seen entering and leaving Boehner's office as the speaker tried to generate the necessary support. A floor debate on the plan was cut short, and the House moved on to discuss the naming of a post office in Illinois.

Staff members were later seen carrying pizzas from a local restaurant into Boehner's office.

Defeat of the measure would be a major setback for Boehner, who assumed his post in January, and further muddy the already tense negotiations over a deficit reduction deal that would also increase the federal borrowing limit. In particular, it would show Boehner was unable to control the tea party conservatives elected last year in a Republican wave that delivered a GOP majority in the House and his ascension to speaker.

Earlier, Boehner declared to reporters that the measure would pass, but McCarthy, R-California, only would say progress was being made in rounding up the votes.

Another speaker at the news conference, Republican Rep. Renee Ellmers of North Carolina, let slip there's more work to be done, calling on House colleagues "who may not be there yet" but were "moving forward on those votes."

Whether Boehner can push the measure through remains an open question. Tea party-backed conservatives staged a virtual revolt against the bill over the past two days, complaining that it doesn't do enough to shrink the size of government and stem the tide of Washington's red ink.

"We don't have the votes yet, (but) we're going to get it passed," Boehner declared Thursday morning to his caucus, according to one Republican source who spoke on condition of not being identified.

Some Republicans have said this will be their last, best proposal. Senate Democrats, however, have warned the plan is dead on arrival on their side of Capitol Hill even if it passes the House.

Reid declared that the Senate was prepared to immediately vote on -- and defeat -- the speaker's plan, assuming the House approves it.

"There are things that either side cannot get," Reid said Thursday morning, adding that Republicans need to "accept that and move on." Sen. Chuck Schumer, D-New York, called Boehner's proposal "a futile gesture."

GOP leaders responded by accusing the Democrats of playing political games.

"When is somebody on the other side of the aisle going to say yes?" Boehner asked. "We have a reasonable, responsible (plan). Let's pass this bill and end this crisis."

Senate Minority Leader Mitch McConnell, R-Kentucky, warned that "Democrats are playing with fire here."

"It's hard to conclude that they're doing it for any other reason than politics," he said.

White House Chief of Staff Bill Daley told CNN on Thursday that, presuming the Boehner plan wins House approval and gets blocked in the Senate, the next step is for everyone "to take a step back in the Congress and look at where is a point of compromise."

Daley said that similarities between the Boehner plan and a competing proposal offered by Reid "may be the grounds for a deal that, hopefully, both parties can pass."

Both the House and Senate planned to work through the weekend, and officials say ongoing behind-the-scene talks will continue.

As the political maneuvering continues, the clock continues to tick down. If Congress fails to raise the current $14.3 trillion debt ceiling by August 2, Americans could face rising interest rates and a declining dollar, among other problems.

Some financial experts have warned of a downgrade of America's triple-A credit rating and a potential stock market plunge. The Dow Jones Industrial Average fell nearly 200 points Wednesday, but opened positively Thursday on the basis of encouraging news from job and housing markets.

Without an increase in the debt limit, the federal government will not be able to pay all its bills next month. President Barack Obama recently indicated he can't guarantee Social Security checks will be mailed out on time.

Regardless, some conservatives insist they won't back the Boehner plan or anything short of deep spending cuts, caps on future spending and a balanced budget to the U.S. Constitution. Rep. Phil Gingrey, R-Georgia, told CNN on Thursday morning that he's not on board.

"I love my speaker, (but) we just keep spending," Gingrey complained. A balanced budget amendment is "the only way we can constrain ourselves," he said.

However, one of the GOP's party elders, Arizona Sen. John McCain, argued Wednesday that it's "worse than foolish" to suggest the current Congress will pass such an amendment by August 2. It's "bizarro," McCain said.

Leaders of both parties now agree that any deal to raise the debt ceiling should include long-term spending reductions to help control spiraling deficits. But they differ sharply on both the nature and timetable of the cuts. Republicans are seeking another vote on the debt ceiling before the 2012 election; Democrats call the demand a political nonstarter and economically destabilizing.

The Boehner and Reid plans both suffered setbacks earlier this week when the nonpartisan Congressional Budget Office released reports concluding that they fell short of their stated deficit reduction goals.

Specifically, the CBO concluded that Boehner's plan would cut spending by $850 billion rather than the $1.2 trillion proponents claimed it would save, which was below the $900 billion increase in the debt ceiling included in the measure.

Boehner has since revised his plan, and the CBO now estimates it would generate a total of $917 billion in savings over the next decade, an increase of about $65 billion over the initial version.

With the revisions, Boehner's proposal now meets his pledge to match any debt ceiling hike with dollar-for-dollar spending cuts.

Boehner's plan would require two separate votes by Congress, allowing for a combined debt ceiling increase of up to $2.5 trillion. In addition to imposing nearly $1 trillion in spending reductions, it would create a special congressional committee to recommend additional savings of $1.6 trillion or more.

Any failure on the part of Congress to enact mandated spending reductions or abide by new spending caps would trigger automatic across-the-board budget cuts.

The plan also calls for a congressional vote on a balanced budget amendment to the Constitution by the end of the year.

Boehner has promised anxious conservatives votes on two versions of a balanced budget amendment on Friday, according to GOP leadership sources.

One version, if adopted by the states, would require Washington to maintain a balanced budget. The other version, one that conservatives have long been pushing, would also require a super-majority vote in both chambers to approve any tax increases.

As for Reid's plan, a CBO analysis released Wednesday concluded it would reduce deficits over the next decade by $2.2 trillion -- $500 billion short of promised savings of $2.7 trillion. Democrats had been claiming their plan would meet the GOP's demand that total savings should at least match any debt ceiling hike through 2012.

Michael Steel, a spokesman for Boehner, said Wednesday that the CBO analysis of Reid's proposal "shows the Senate plan for what it is: a grab-bag of gimmicks that gives the president a blank check."

Democrats responded by arguing that Reid's plan has more guaranteed savings than Boehner's. They also promised that the final version of Reid's bill will include more savings.

Reid's plan would cut spending by $1.8 trillion as part of the total $2.2 trillion in savings, according to the CBO. Roughly $1 trillion in the savings are based on the planned U.S. withdrawals from military engagements in Afghanistan and Iraq.

Limiting future discretionary spending would save another $751 billion, and an estimated $375 billion would be saved in interest payments due to reduced borrowing because of the spending cuts.

Reid's plan also would establish a congressional committee made up of 12 House and Senate members to consider additional options for debt reduction. The committee's proposals would be guaranteed by a Senate vote with no amendments by the end of the year.

Among other things, Reid has stressed that his plan meets the key GOP demand for no additional taxes. Boehner, however, argued this week that Reid's plan fails to tackle popular entitlement programs such as Medicare, which are among the biggest drivers of the debt.

Beneath the harsh partisan rhetoric, there have been signs of a growing recognition of a need for further compromise. McConnell called Tuesday for renewed negotiations with Obama, and indicated that his party must be willing to move away from some of its demands.

Sources close to the negotiations have told CNN that Vice President Joe Biden is very much in the mix of the back-channel conversations that are occurring on a possible fallback position.

Obama made a nationally televised plea for compromise Monday night.

A CNN/ORC International Poll reveals a growing public exasperation and demand for compromise. Sixty-four percent of respondents to a July 18-20 survey preferred a deal with a mix of spending cuts and tax increases. Only 34% preferred a debt reduction plan based solely on spending reductions.

According to the poll, the public is sharply divided along partisan lines; Democrats and independents are open to a number of different approaches because they think a failure to raise the debt ceiling would cause a major crisis for the country. Republicans, however, draw the line at tax increases, and a narrow majority of them oppose raising the debt ceiling under any circumstances.

CNN's Ted Barrett, Kate Bolduan, Gloria Borger, Keating Holland, Brianna Keilar, Jeanne Sahadi, Xuan Thai, Jessica Yellin and Deirdre Walsh contributed to this report.