Boehner's latest offer broke a long impasse. It calls for about $450 billion in revenue from increasing the top rate on million-dollar-plus income from 35 percent to the Clinton-era rate of 39.6 percent.

The additional revenue required to meet the $1 trillion target would be collected through a rewrite of the tax code next year and by slowing the inflation adjustments made to tax brackets.

In return, Boehner is asking for $1 trillion in spending cuts from government benefit programs like Medicare. Those cuts would defer most of a painful set of across-the-board spending cuts set to slash many domestic programs and the Pentagon budget by 8-9 percent, starting in January.

Boehner's proposal was described Sunday by officials familiar with it. They required anonymity because of the sensitivity of the talks.

Boehner also continues to press for a less generous inflation adjustment for Social Security benefits, a move endorsed by many budget hawks. Obama and Democrats on last year's deficit "supercommittee" endorsed the idea in offers made last year, but they're more reluctant now.

The new inflation adjustment would also raise about $70 billion over a decade in new revenues because tax brackets would rise more slowly for inflation, driving people more quickly into higher tax brackets.

The increased optimism come as time is running out before the adjournment of Congress. Tax rates on all workers go up in January, and $109 billion worth of across-the-board spending cuts begin to take effect then as well. Taken together with the expiration of extended jobless benefits and a 2-percentage-point break in Social Security payroll taxes, the combination of austerity steps threatens to send the economy back into recession.

The burst of optimism is tempered by the caution that the remaining steps to reaching a deal â¿¿ particularly how much to cut Medicare and whether to impose the new, less generous inflation adjustment to Social Security â¿¿ are difficult. Then comes the job of selling it to a polarized Congress, where GOP conservatives have been railing against higher tax rates for months as sure to cost jobs and hurt small business, and Democrats have taken a harder line against cost curbs to Medicare.

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