US Treasury Secretary Timothy Geithner says a 2 August deadline on increasing the US debt limit cannot be extended.
He said that if Congress did not agree to raise the ceiling beyond the current $14.3tn (£8.9tn), there would be catastrophic damage to the economy.
President Barack Obama is to discuss a debt deal with Congressional leaders.
House Speaker John Boehner said he favoured setting a less ambitious target than an earlier proposal of a comprehensive $4tn debt reduction.
The US faces running out of money and defaulting if Congress does not allow the government to take on more debt.
If no agreement is reached, the government would be unable to pay civil servants, government contractors, pensioners or holders of government debt.
Economists and the White House have warned that such a default could push the US back into recession and have a global economic impact.
When the Congressionally-set debt limit has been reached in the past, Congress has voted to raise it.
This year, however, newly empowered Republicans are determined to prevent any tax increases and want to see aggressive measures to reduce the deficit in exchange for agreeing to raise the debt ceiling.
In a round of interviews before Mr Obama’s meeting with Congressional leaders on Sunday, Mr Geithner said the US would not default.