A week of high brinkmanship on Capitol Hill opened today with neither side in the impasse over the US debt ceiling prepared to budge and with the US just days away from a potentially catastrophic default.

The White House called a temporary cessation of hostilities, with meetings that have been going on almost solidly for more than a week suspended over the weekend to allow tempers to cool. But despite the hiatus, there was no sign from either the Republicans or Democrats that they were preparing to compromise.

In interviews on the Sunday political shows, the White House budget director, Jack Lew, made clear that tax rises for the rich would have to be on the table – a demand that the Tea party-steeled Republicans have doggedly refused to contemplate. "Can we get a balanced package together? It's not fair to ask senior citizens to pay a price, to ask families paying for the college education of their children to pay a price, but leave the most privileged out of the equation," he told ABC's This Week.

Lew said he was confident a deal would be done but criticised right-wing Republicans, who are taking the crisis to the brink. "The debt will be extended. Notwithstanding the voices of a few who are willing to play with Armageddon, responsible leaders in Washington are not."

Those "voices of a few" include that of the presidential candidate Michele Bachmann, who confirmed last week that she would vote against raising the debt ceiling, whatever the outcome of the talks.

The US treasury has until 2 August to raise the limit on its debt from the current $14.3tn (£9tn) or risk running out of federal money immediately. Analysts say that in order to give Congress time to prepare the legislative paperwork needed to raise the ceiling, a deal would have to be close to fruition by as early as this Friday.

Despite the fast-approaching deadline, Republicans are steadfastly refusing to play ball with President Obama's compromise package, which would involve $4tn of deficit cuts including $1tn that would come from increased taxes.

John Kyl, the Republican whip in the senate, said on This Week: "Unless the president gets off his absolute obsession with raising taxes, Republicans will not do anything that will harm our economy. Job-killing taxes will harm our economy."

Mitch McConnell, Republican leader in the Senate, put forward a get-out-of-jail plan last week that would allow Obama to push through an increase in the debt ceiling with only minority support from Congress – a move that would in effect postpone the big debate on the deficit until after next year's presidential election.

But the plan is only increasing dissension within the Republican party. Jim Jordan, chairman of the Republican study committee, called McConnell's proposals a cop-out. "I'm not going to support the McConnell plan. This is just kicking the can down the road," he told Fox News.