Republicans will keep working to avoid the so-called fiscal cliff of tax rises and spending cuts, House Speaker John Boehner has said.
Earlier, right-leaning Republicans rejected a plan by Boehner to raise taxes on higher earners.
Boehner said “significant spending cuts and real tax reforms” were needed.
President Barack Obama said he believed a deal could still be done to beat the 1 January deadline, and called for everyone to “give a little bit”.
Analysts say the Republicans’ rejection of Boehner’s plan has weakened his position in negotiations with the Obama administration.
Boehner’s plan would have had little chance of passing a Senate vote.
It was seen as an effort to tell the US public that the Republicans should not be blamed if a deal could not be reached.
The House is controlled by the Republicans, but the Senate is Democrat-led.
At a news conference, Boehner conceded the House’s failure to take up the tax bill was not the outcome that he wanted.
He said “God only knows” how the cliff would be avoided, but Republicans would keep working on a plan to protect families and small businesses.
“We only run the House. Democrats continue to run Washington,” he said.
If politicians fail to agree new fiscal rules by the end of year, steep tax rises and deep spending cuts are meant to take effect automatically.