The president’s proposal does stick to the broad framework of the deal Mr. Boehner wants: an upfront deficit-reduction “down payment” that would serve to cancel the automatic tax increases and spending cuts while still signaling seriousness on the deficit, followed by a second stage in which Congress would work next year on overhauling the tax code and social programs to secure more deficit reduction.

But the details show how far the president is ready to push House Republicans. The upfront tax increases in the proposal go beyond what Senate Democrats were able to pass earlier this year. Tax rates would go up for higher-income earners, as in the Senate bill, but Mr. Obama wants their dividends to be taxed as ordinary income, something the Senate did not approve. He also wants the estate tax to be levied at 45 percent on inheritances over $3.5 million, a step several Democratic senators balked at. The Senate bill made no changes to the estate tax, which currently taxes inheritances over $5 million at 35 percent. On Jan. 1, the estate tax is scheduled to rise to 55 percent beginning with inheritances exceeding $1 million.

Administration negotiators also want the initial stage to include an extension of the payroll tax cut or an equivalent policy aimed at working-class families, an extension of a business tax credit for investments, and the extension of a number of other expiring business tax credits, like the one on research and development.

To ensure that there are no more crises like the debt ceiling impasse last year, Mr. Geithner proposed permanently ending Congressional purview over the federal borrowing limit, Republican aides said. He said that Congress could be allowed to pass a resolution blocking an increase in the debt limit, but that the president would be able to veto that resolution. Congress could block a higher borrowing limit only if two-thirds of lawmakers overrode the veto.

In total, Mr. Geithner presented the package as a $4 trillion reduction in future deficits, but that too was disputed. The figure includes cuts to domestic programs agreed to last year that the White House put at $1.2 trillion but that Republicans say is about $300 billion less. And it counts savings from ending the wars in Iraq and Afghanistan, even though no one has proposed maintaining war spending over the next decade at the current rate.

“Listen, this is not a game,” Mr. Boehner said. “Jobs are on the line. The American economy is on the line. And this is a moment for adult leadership.”

Senate Democratic leaders left their meeting with Mr. Geithner ecstatic. If the Republicans want additional spending cuts in that down payment, the onus is on them to put them on the table, said Senator Harry Reid of Nevada, the Democratic leader.