WASHINGTON — President Obama tried on Sunday to revive the chances for a sweeping budget agreement to reduce the nation’s deficit and repair its perilous finances, but Congressional Republicans continued to balk, insisting on a more modest deal to avert a default on the national debt.

Mr. Obama, meeting with leaders from both parties at the White House, bluntly challenged Republicans a day after Speaker John A. Boehner pulled back from a far-reaching agreement aimed at saving as much as $4 trillion over 10 years, officials briefed on the negotiations said. The meeting ended after an hour and 15 minutes with little progress, but the two sides agreed to resume talking Monday, and every day after that, until a deal is done.

White House officials said Mr. Obama was still determined to pursue the boldest package possible — one that would require new tax revenue as well as cuts in Medicare and other entitlement programs — but he faces steadfast opposition from Republicans and growing qualms among Democrats.

“Congress has to act,” Treasury Secretary Timothy F. Geithner said on the CBS News program “Face the Nation.” “If they don’t act, then we face catastrophic damage to the American economy, and the leadership, to their credit, and I mean Republicans and Democrats, fully understand that.”