Barack Obama, Republicans fail to agree on deal to stave off debt default
"He's been very clear. He will not pay ransom in exchange for the Republicans in the House doing their job," Mr Carney said.
Many rank-and-file Republicans also appeared to be sceptical of Mr Boehner's plan.
Mr Boehner's grip over his troops has been tenuous this year, and many of the chamber's most conservative lawmakers have repeatedly defied him on other crucial votes.
The Obama administration says it will be unable to pay all of its bills if Congress does not raise the $16.7 trillion debt ceiling by October 17.
Treasury secretary Jack Lew said he would be unable to prioritise some payments over others among the 30 million transactions his department handles each week.
Opinion polls indicate that Republicans appear to be getting more of the blame for the standoff.
The Republican Party's approval rating now stands at a record low of 28 per cent, according to Gallup, down 10 points from pre-shutdown levels.
The Democratic Party's approval rating has dipped slightly to 43 per cent.
News of a possible deal sparked optimism on Wall Street, with all three major equity indices trading higher overnight.
