WASHINGTON — President Obama delivered to Speaker John A. Boehner a new offer on Monday to resolve the pending fiscal crisis, a deal that would raise revenues by $1.2 trillion over the next decade but keep in place the Bush-era tax rates for any household with earnings below $400,000.

The offer is close to a plan proposed by the speaker on Friday, and both sides expressed confidence that they were closing in on a major deficit-reduction plan that could be passed well before January, when more than a half-trillion dollars in automatic tax increases and spending cuts would kick in.

Senior Republican aides said the speaker was to meet with House Republicans on Tuesday morning to discuss the state of negotiations. But they cautioned that obstacles remained.

“Any movement away from the unrealistic offers the president has made previously is a step in the right direction,” said Brendan Buck, a spokesman for Mr. Boehner. “We hope to continue discussions with the president so we can reach an agreement that is truly balanced and begins to solve our spending problem.”