Congress this week will begin taking the first steps toward a more structured and orderly budget process, beginning what both parties hope is a move away from the vicious cycle of deadline-driven quick fixes.
In the Senate, Democrats were putting the finishing touches on a budget they plan to introduce on Wednesday, their first in four years, while House Republicans were preparing to introduce a spending plan of their own on Tuesday morning.
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The two proposals, which would set spending targets for the fiscal year that begins Oct. 1, will be miles apart ideologically and difficult to merge. Democrats plan to rely heavily on closing tax loopholes that benefit corporations and the wealthy to produce new revenue, while Republicans will focus on slashing spending to balance the budget in 10 years.
But the fact that both houses of Congress are working on their budgets simultaneously after years of impasse raised some measure of hope — albeit slight — that Democrats and Republicans might be able to work out some sort of compromise.
Compromise between the two parties, however, is only half of a more complicated bargain. Democrats also have to bridge the divide among a politically diverse group of Democrats on the Senate Budget Committee.
The committee chairwoman, Senator Patty Murray of Washington, said Monday that she expected all 12 members of her majority to vote in favor of the Democrats' budget, even if some members so far remain uncommitted.
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"I have a really diverse committee," Mrs. Murray said, adding, "They all recognize that we have some really common goals, and we have worked it out."
That diversity is one of the major reasons Senate Democrats have not written a spending plan of their own since 2009, given the challenge of bringing together senators from Oregon to Virginia to Vermont who do not always agree on issues like whether cuts should fall more heavily on military or nonmilitary programs, and which tax loopholes to eliminate.
"Dealing with the difference of opinion is tough," said Senator Bernard Sanders of Vermont, an independent who has tried to ensure that the Democrats' budget does not include an adjustment to the inflation rate that would calculate it in a way that would decrease federal benefits. Mr. Sanders said he was confident the inflation rate calculation would be untouched, but he was not prepared to sign on to Mrs. Murray's plan until he sees the final document.
"We've had long talks; we'll see what happens," he said.
The committee is closely divided between 12 Democratic votes and 10 Republican votes.
In another sign that both parties continue to look for ways to meet in the middle, President Obama is to visit Capitol Hill for four separate meetings this week with the Democratic and Republican conferences of both houses. The president and his aides have said that this rare display of bipartisan outreach, coming a week after Mr. Obama dined with a dozen Republican senators, is intended to help foster cooperation between the parties.
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Against this backdrop, the Senate Appropriations Committee was preparing to lay out a separate stopgap spending plan to keep the government financed through September. The House passed its plan last week.
Senator Harry Reid, the majority leader, who framed the Senate's action as a first step in a longer process, said, "This week will offer another opportunity for the Senate to return to regular order, an opportunity for this body to legislate through cooperation, through compromise, as we used to do."
"This legislation," Mr. Reid continued, "will be a test of the Senate's good will. America's economy is poised to grow and expand. The last thing it needs is another manufactured crisis such as a government shutdown to derail its progress."
The movement expected in Congress this week will draw attention to one of the more unusual aspects of business in Washington. When it comes to writing budget resolutions, the House and the Senate have worked on entirely separate paths. Senate Democrats, unable to always agree and not eager to take votes that could prove politically unpopular, have avoided drawing up large-scale a budget.
House Republicans, meanwhile, have made the budget the focus of their efforts. And they have seized on the issue as a way of portraying Democrats as inept and unfocused.
The National Republican Senatorial Committee snidely commented on Monday that Democrats had claimed "for more than 1,400 days that the dog ate their homework." And Republican senators have churned out news releases noting what could have been accomplished since the Democrats last passed a budget, like 179 round-trip missions to the moon and 292 expeditions to the summit of Mount Everest.
But even if Democrats do pass a budget in the Senate, it will mean little unless it can be merged with the House Republican budget and pass both houses of Congress.
"I think because of all the attention on the failure to pass a budget in regular order, Democrats are at least obligated to," said Senator Benjamin L. Cardin, Democrat of Maryland, who was until recently a member of the Budget Committee.
"But I don't think there's much optimism that we're going to reconcile a budget with this House quickly," he added.