Washington — Only a few months ago Democrats and Republicans on Capitol Hill were wrestling bitterly over social security. The federal budget process seemed ready for the scrap heap. And as record numbers of Americans lost their jobs, Washington bickered over a response and did nothing.
Now, with relatively little fuss, the nation's lawmakers are moving on all of those fronts. In its first three months, the fleet-footed 98th Congress may complete a big chunk of its work for the year:
* A rescue for the social security system, the biggest task of all for the new Congress, loped through the House last week and is expected to win passage through the Senate before the Easter recess begins March 25.
* A jobs and relief bill will probably arrive this week on the President's desk, despite a last-minute snafu in the Senate. Freshman Sen. Robert Kasten (R) of Wisconsin is leading a one-man crusade to attach an amendment repealing tax withholding for interest and dividends. Such an amendment would guarantee a presidential veto.
The jobs bill may be pushed along by a deadline on Tuesday, the day more than half the states run out of funds for unemployment benefits that would be provided by the legislation.
If it does become law, the jobs bill will include too much spending for some conservatives and not enough for Democrats from hard-hit areas. But the package is a testament to the new Congress's ability to find the middle ground.
* The first budget resolution, which last year tied Congress up in knots, is expected to be completed on the House and Senate floors before Easter, one month ahead of the deadline. Although the '84 budget offers the opportunity for party friction, both sides are optimistic that they can come up with a workable plan.
The oil that is keeping the legislative machinery running so smoothly is cooperation between the two parties.
''We have been able to accomplish several things in bipartisan agreement,'' explains an aide to senate majority leader Howard H. Baker Jr. Despite their considerable differences, the Republican senator from Tennessee and Democratic House Speaker Thomas P. O'Neill Jr. of Massachusetts have established a working relationship that seems to benefit each.
''The peace (between the parties) is based on a coincidence of interests,'' says Christopher Matthews, an aide to Speaker O'Neill. Both parties needed to repair the financial problems of social security, and both wanted a jobs bill.
Some of the most liberal Democrats are complaining that the party is compromising too much, Mr. Matthews says. He responds, ''The speaker's a fighter , but when you can accomplish your agenda without a fight, why fight?''
Democrats will attempt to sharpen party lines this week as the House Budget Committee begins writing its version of the federal budget. The President is pushing for a 10 percent growth rate for defense, after discounting for inflation. In a questionnaire sent out by House Budget chairman James R. Jones (D) of Oklahoma, more than 80 percent of the Democratic representatives favored 3 to 5 percent growth.
But even on the defense budget, Democrats may have trouble picking a fight with Republicans.
Senate budget chairman Pete V. Domenici has called for a 5 percent growth rate. The Republican New Mexico senator has delayed committee action to give the President a few days to make his case for a higher defense figure, but Mr. Reagan is battling a strong sentiment in his own party to slow down military spending.
While Democrats in the House talk of writing a truly Democratic budget, their counterparts in the Senate are talking bipartisanship.
The lines between the two parties have become blurred in the Republican-controlled Senate Budget Committee. The new ranking Democrat, Lawton Chiles of Florida, is a genial, moderate-to-conservative senator who wants the budget committee to return to its earlier days of bipartisanship.
Senator Chiles is also a close friend of Chairman Domenici, and the two have been in frequent consultation.
''I think we (Democrats) are going to have some input because the Republicans find themselves divided this time,'' Senator Chiles said in an interview. ''Before, they brought (the budget) to us as a fait accompli. This time they're not able to do that.''
''It looks like there's just no way either side can pass a budget without help from the other side,'' says Chiles, who expects a separate vote on each function in the budget, with a different coalition on every vote.
If there is an off-key note in the harmony on Capitol Hill, it will probably involve taxes. Democrats in both houses want to raise more revenues than either the White House or the Republicans.
Among House Democrats, about 98 percent reported to Chairman Jones that they would prefer eliminating or reducing the 10 percent income tax cut scheduled for July 1. And nearly 80 percent favored repeal of ''tax indexing,'' a measure scheduled to begin in 1985 to prevent taxes from rising with inflation.
On the Senate budget committee, Democrats hold similar views, according to Chiles. He says they may win enough Republican votes to cancel indexing, estimated to cost the US Treasury $40 billion by 1988.
If both Senate and House budget committees stay on schedule, they will take their budgets to the floors of their respective houses this month. When Congress returns from the Easter recess, a joint Senate-House conference will work out the differences, and the budget resolution will be in place an unprecedented one month ahead of time.
Perhaps Congress will even finish up its work soon enough to fulfill Senator Baker's dream, which is to send the Senate home for July and August. But if legislation presents little partisan strife, Baker's proposal to end early might. Some Democrats see it as an effort to give Republican senators a running start on their reelection campaigns.
''Some Democrats are sort of alarmed about the fast track,'' Chiles says, because they see the two-month break helping Republican senators (19 of whom are up for reelection in 1984). The Florida senator says he would be ''surprised'' if Congress finished its work in time. ''A lot of things happen on the way to the forum,'' he says.