Kevin McCarthy, the House speaker, called on Joe Biden to agree to compromises and spending cuts, as the two remain deadlocked over raising the nation’s $31.4tn debt ceiling.

McCarthy spoke on Monday before Biden gives the annual State of the Union address to a joint session of Congress on Tuesday, aiming to get ahead of the president and reinforce his role as the leading congressional negotiator.

The White House has said Biden will discuss federal spending cuts with Republicans, but only after the debt ceiling is lifted, while McCarthy has said Republicans will only lift the ceiling if Biden agrees to spending cuts. While the two sides disagree on the order of the subjects they are tackling, both say they will continue to talk.

“Mr President, it’s time to get to work,” said McCarthy, whose Republicans won a narrow majority in the House of Representatives in November’s election.

“We must commit to finding common ground on a responsible debt limit increase. Finding compromise is exactly how governing in America is supposed to work, and exactly what the American people voted for just three months ago,” McCarthy said.

“Defaulting on our debt is not an option, but neither is a future of higher taxes, higher interest rates and an economy that doesn’t work.”

House Republicans want to use the debt ceiling, which covers the spending programs and tax cuts Congress previously approved, as leverage to push spending cuts, after two years of Democratic control of the House and the Senate.

Biden on Tuesday is expected to insist that raising the debt limit is not negotiable and US lawmakers should not use it as a “bargaining chip”, his top economic adviser, Brian Deese, said on Monday.

“This bedrock idea that the United States has met all of its financial obligations for its existence as a country isn’t something that anybody should be using as a bargaining chip. It’s not a negotiable item,” Deese said.

Biden seemed to question McCarthy’s ability to keep Republicans in line last week, calling McCarthy “a decent man, I think”, but noting the concessions he made to become speaker in January. Those included changing a rule of the chamber to allow any member to call for a vote that would remove him, rather than requiring a majority from either party.

Despite what appears to be a standoff, McCarthy emerged from a meeting with Biden last week saying he believed the two could find common ground.

A day later, McCarthy told reporters that the president had agreed to meet again.

The White House press secretary, Karine Jean-Pierre, said the White House had been in touch with McCarthy’s staff on next steps.