Rep. Steny H. Hoyer, the second-highest ranking Democrat in the House, noted that tax breaks and spending cuts could be dealt with retroactively once an agreement is struck. Washington has frequently done that in the past few years.
"Sequestration will be harmful to Maryland, but it will also be harmful to the country, which is why I think it's so important that we act," the Southern Maryland lawmaker said in an interview. "If we don't take care of sequestration in the next few hours, then there's no doubt that it will be a subject [dealt with] immediately" in the new year.
McConnell and Biden had been in close contact all day after having worked past midnight Sunday and then resumed again early Monday morning to craft the deal.
The minority leader convened Republican senators behind closed doors at dinner time, and many emerged optimistic that a deal was at hand.
"Hope springs eternal around here, even though it gets a little sticky at times," said Sen. Pat Roberts, a Kansas Republican. Boehner similarly convened his troops in a basement office beneath the Rotunda.
One result became increasingly clear: With many issues still unresolved, Washington was poised to continue the partisan budget battles that have defined Obama's first term well into this year.
Under the proposed deal, more than $660 billion in revenue would be raised — far less than the $1.6 trillion Obama first sought in new revenue when he still hoped for a large deficit-reduction package.
The agreement would set the top tax rates at 39.6 percent for income above $450,000 for households and $400,000 for individuals.
Tax rates on investment income would also rise for those higher-income households, from the historic low 15 percent rate on capital gains and dividends to 20 percent. The president had wanted to tax dividends at the same rate as ordinary income.
About 2 million out-of-work Americans would benefit, if the deal is approved, from a one-year extension of long-term unemployment benefits, which expired over the weekend.
One area that hewed closer to Democratic priorities was Obama's proposal to reinstate limits on how much upper-income households can benefit from personal exemption tax credits and itemized deductions. Those limits, in place before the George W. Bush-era tax cuts began in 2001, were done away with over the past decade.
The agreement under consideration would reduce those deductions for households earning more than $250,000. That would lead to higher effective taxes on those households without an increase in their tax rates, which Republicans had resisted.
Other tax credits established under Obama's economic recovery program would also be extended for five more years. That provision is a nod to Democratic calls for more stimulus spending to help the economy and for adjustments to the tax code to help those with more modest incomes.
Those credits include a $2,500 tax credit for college students and additional credits that allow cash refunds even if no tax is owed for those with children and family incomes below $45,000.
The deal also includes a permanent fix for the Alternative Minimum Tax, a part of the tax code that was established decades ago to ensure high-income earners pay at least a minimum amount of tax, rather than substantially eliminate their liability with extensive deductions. But it increasingly snares middle-class families because it was never indexed to inflation. Congress must fix the Alternative Minimum Tax issue every year, a problem that would be finally resolved with Monday's deal.
Even with these thorny tax issues all but settled, the mandatory budget cuts that would start to reduce federal spending Wednesday remained a sticking point until late Monday.
The sequestration cuts slice across defense and domestic programs and had been set as a last-ditch trigger designed to spur negotiations for a broader budget deal after an earlier deficit-reduction effort failed.
Talks focused on postponing the cuts for two months, but offsetting the $24 billion that would not be saved. The White House and Republicans eventually settled on a mix of revenue increases and spending cuts.
Postponing the automatic cuts for two months, as the Republicans wanted, all but ensures the budget battles will continue. Democrats had hoped to postpone that reckoning for a year to keep Obama's second term from beginning with a repeat of past tumultuous budget battles.
Baltimore Sun reporter Michael Dresser contributed to this article.