Newly re-elected, President Obama moved quickly on Wednesday to open negotiations with Congressional Republican leaders over the main unfinished business of his term — a major deficit-reduction deal to avert a looming fiscal crisis — as he began preparing for a second term that will include significant cabinet changes.

Mr. Obama, while still at home in Chicago at midday, called Speaker John A. Boehner in what was described as a brief and cordial exchange on the need to reach some budget compromise in the lame-duck session of Congress starting next week. Later at the Capitol, Mr. Boehner publicly responded before assembled reporters with his most explicit and conciliatory offer to date on Republicans’ willingness to raise tax revenues, but not top rates, together with a spending cut package.

“Mr. President, this is your moment,” said Mr. Boehner, a day after Congressional Republicans suffered election losses but kept their House majority. “We’re ready to be led — not as Democrats or Republicans, but as Americans. We want you to lead, not as a liberal or a conservative, but as president of the United States of America.”