Republicans postponed a vote on the latest plan to cut spending and lift the debt limit on Thursday.
The vote on House Speaker John Boehner's bill was expected at about 6 p.m. ET, but it was postponed as Republican leaders failed to rally sufficient support.
Around 10:30 p.m. ET, House majority whip Kevin McCarthy told reporters that there would be no vote Thursday night.
So-called Tea Party Republicans want bigger spending cuts than Boehner proposes, and may also be holding out for a constitutional amendment requiring a balanced budget. Many Republicans were seen going in and out of Boehner's office Thursday evening after the vote was postponed, CNN reported.
Asked what he and the Speaker had talked about, Jeff Flake, a Republican from Arizona, said, "I think that's rather obvious …There's negotiations going on."
It was not immediately clear how things would proceed Friday.
Republican leaders have been trying to line up the 216 votes the debt bill would need to pass the House, and they have encountered opposition from some conservatives. There are 240 Republicans in the House. Few, if any, Democrats were expected to support the measure.
Even if it does eventually pass, Boehner's bill is expected to be voted down by the Democratic majority in the U.S. Senate, and even if it could pass the Senate, it would face a White House veto threat.
The Treasury Department has insisted that Congress must vote to raise the government's $14.3-trillion borrowing limit by Tuesday or the country will default on its debt obligations.
Before the planned House vote, the chief executives of the largest U.S. financial institutions sent a letter to the White House and to members of the U.S. Congress, urging them to come to an agreement this week.
Bank of America Corp.'s Brian Moynihan, JPMorgan Chase & Co.'s Jamie Dimon, and Goldman Sachs Group Inc.'s Lloyd Blankfein and others warned that the consequences of not acting would be grave for the economy, the job market and U.S. global economic leadership.
"A default on our nation's obligations, or a downgrade of America's credit rating, would be a tremendous blow to business and investor confidence," the letter said.
Treasury prepares spending choices
The U.S. Treasury Department said Thursday it will soon provide more information on which bills it will pay should Congress not raise the government's borrowing limit by Tuesday's deadline.
The government makes more than 70 million payments a month.
The Treasury also said it still planned to go ahead with its regular weekly auction of three-month and six-month treasury bills on Monday, one day before the deadline. The money raised from that auction will go toward redeeming $87 billion in securities that will mature on Aug. 4 and, it said, would not breach the current borrowing limit.
Banks also hold treasury bonds as assets they can easily sell. If their value falls, so does a bank's capital. That could force financial institutions to hold more cash, which in turn means less money available to lend to consumers and businesses.
Currently, U.S. banks hold a total of $1.67 trillion in treasury bonds and mortgage-backed securities combined, according to the Federal Reserve.
At an afternoon news conference, Boehner said the House would act on legislation that he called "a sincere, honest effort to end this crisis."
The delay comes amid growing worry that a Congress divided along partisan and ideological lines might remain gridlocked past the deadline.
Nervous investors sent the Dow Jones industrial average down almost 200 points Wednesday, on top of a 92-point drop the day before.
Even if the U.S. doesn't default, investors worry that the country might lose its triple-A credit rating. That could raise interest rates and possibly slow down the U.S. economy, which is still recovering from the worst recession in decades.
"We're running out of time," said Phil Dow, director of equity strategy at RBC Wealth Management in Minneapolis. "It's getting scary."
"Default will rock our financial system to its core," Senate Democratic majority leader Harry Reid said at the start of Thursday's Senate session.
Earlier, Reid said the Senate would vote on the Boehner bill as soon as the House finished — and predicted it would fail in his chamber.
"No Democrat will vote for a short-term Band-Aid that would put our economy at risk and put the nation back in this untenable situation a few short months from now," Reid said.
If Boehner's plan does fail in the Senate, Reid could then try to push through his own proposal or make changes to the Boehner plan to make it more acceptable to the Democrats.
In a commentary Thursday, BMO Financial Group chief economist Sherry Cooper predicted the debt ceiling would be raised early next week, averting a government shutdown and default.
Citing unidentified Washington sources, Cooper suggested two options exist for heading off a default.
Compromise talks said to be underway
Reid and Republican Mitch McConnell, the Senate minority leader, are "already working on ways to bridge the gaps between and House and Senate bills and craft an alternative that could pass both chambers by Aug. 2," Cooper said.
The other option kicks in after the Senate votes on Reid's bill. At that point, both the House and Senate plans go to a joint conference committee to try to resolve their differences.
In reality, Cooper said, those negotiations are already underway, "so the ultimate compromise will be ping-ponged quickly between both chambers until a final agreement can be reached, likely by early next week, avoiding a government shutdown and default."
While the Boehner and Reid measures differ in key details, they also share similarities that underscore the concessions made by the two sides in recent days.
Reid's bill does not include a tax increase to reduce deficits, a bow to Republicans.
But neither does the House measure require passage of a constitutional balanced budget amendment, a step in the direction of Obama and the Democrats.
The possibility of a ratings downgrade has arisen because agencies such as Standard and Poor's have said that $4 trillion in cuts over 10 years is needed for the U.S. to hold on to its top-tier, triple-A rating.
Cooper suggested a compromise in the range of $2 trillion to $3 trillion would be enough to get rating agencies to refrain from downgrading U.S. debt "at this time."