The Treasury secretary, Jack Lew, warned on Thursday that the continued brinksmanship over the debt limit risks unforeseen consequences in the financial markets that could in turn lead to the US running out of cash within days.

As pressure mounted on Congress to cut a deal before next Thursday's deadline for extending the federal debt limit, Lew accused Republicans of underestimating the danger of inadvertently triggering a stampede among investors that could rapidly drain remaining reserves.

More than $100bn of the US debt, known as Treasury bonds, is typically reissued every week as investors roll over their loans to the government. Typically this process is routine and does not add to the $17tn US debt pile, but simply refinances a portion of it.

But markets have already been spooked by Republican threats to refuse to extend the debt limit if they do not extract concessions on healthcare reform. Short-term borrowing costs nearly tripled in a bond auction on Tuesday as investors feared there was a risk that interest and capital repayments could be missed.

A similar wariness to roll over bonds expiring next week could exhaust a $50bn cash reserve at any point, warned Lew. "Trying to time a debt limit increase to the last minute could be very dangerous," he said in written congressional testimony. "If US bond holders decided that they wanted to be repaid rather than continuing to roll over their Treasury investments, we could unexpectedly dissipate our entire cash balance."

Answering written questions by members of the Senate finance committee, he added: "I very much fear that miscalculation is something that could have devastating consequences. It is impossible to predict with any degree of accuracy when we will run out of money."

Lew's warnings came as House Republicans showed signs of bowing to pressure from donors and business supporters to back down from their threat to withhold a debt limit authorisation unless the White House agreed to first discuss spending reductions.

Republican aides said on Thursday that House speaker John Boehner will ask House Republicans to approve a short-term extension of the government's ability to borrow to meet its bills.

Boehner is due to meet Obama for fresh talks on Thursday afternoon and is expected to urge his conservative colleagues to act before the government runs out of borrowing authority next week.

Republicans have been insistent that budget cuts and other measures be added to the so-called debt ceiling legislation but the aides wouldn't say whether he'll seek to add other material to the measure.

The aides required anonymity to reveal the information before Boehner makes an announcement after a closed-door meeting with his GOP colleagues.

Lew warned that if they failed to reach a deal it would be impossible to "prioritise" certain bills due next – as some Republicans have urged – because computer systems made it impossible to selectively refuse some spending obligations but not others.

"Between October 17 and November 1, we have large payments to Medicare providers, social security beneficiaries, and veterans, as well as salaries for active duty members of the military," he said. "A failure to raise the debt limit could put timely payment of all of these at risk."

Some Republicans on the committee accused Lew of exaggerating the risks of debt limit breach compared the broader problems of excessive debt.

But Democratic committee member Ron Wyden said the repercussions of default were hard to overstate. "In the event of a default or near default, the dominoes are going to fall fast and hard."

The Associated Press contributed to this report