The $531.6 billion budget President Carter sent Congress yesterday was obsolete the moment it reached the Capitol steps.

Although the administration's spending and tax proposals still serve as a starting place for the lawmakers' deliberations, Congress now has the staff and machinery for putting its own stamp on the budget.

And the odds are that the two houses will exercise their independence when voting time comes up this session.

Since Congress established a new budget process in 1974, the lawmakers have aimed mainly at imparting order to the appropriations process. But they have rejected presidential requests to cut domestic social programs.

This year, in the wake of California's Proposition 13 and other expressions of voter discontent about government fiscal matters, the heightened congressional interest in the budget could work to Carter's advantage, while at the same time giving him fits.

With many new members elected on a hard-line fiscal platform, Capitol Hill veterans say there's now a better-than-average chance Congress will go along with Carter's overall spending targets -- and his $29 billion deficit as well.

At the same time, however, the betting is that the lawmakers also will seek more than ever to reorder the president's priorities -- that is, to reshape his individual spending recommendations to suit congressional liking.

And that's where the cruch could come.

Moreover, the signs are the debate will be bitter, with both Republicans and Democrats sharply divided on many key issues.

The new preoccupation of Congress with budget issues already has shown up in a scramble by newer members for seats on the House and Senate Budget committees -- posts that previously had to be assigned much like Army K.P.

Congressional factions are geared up for a major guns-vs.-butter debate. Observers say the result could be less money for defense than Carter wants, and fewer cuts in social programs.

The battleground for the year's biggest fiscal fight will be the congressional budget process, set up in late 1974 to help the lawmakers with economic and budget policy-making.

Under the procedure, the House and Senate pass a joint resolution each spring agreeing on the economic policy the government should follow and setting specific tax and spending targets to carry it out.

The two houses then pass their appropriations bills, adhering as closely as possible to those budget targets. In September, they take another look at the economy and the budget picture. Then they set binding ceilings on spending.

The new budget-making machinery was established primarily in response to then-President Nixon's attacks on Congress' budgetary excesses. Nixon, declaring Congress hopelessly spedthrift, impounded $8 billion in appropriations.

At that time, the president's budget each January was far more crucial to Congress' operation. With Congress devoid of any budget-making machinery, the White House had a monopoly that gave it inordinate clout.

Hill leaders decided they needed a new procedure for the budget -- both to ward off Nixon's "big spender" charges and to prevent the White House from usupring their power over the pursestrings.

Before the new procedure, appropriations bills were passed willy-nilly, often several months late, and the lawmakers had no real idea how their individual decisions affected the total.

The procedure hasn't yet resulted in any major congressional budget-paring from the totals President Ford -- and later President Carter -- have proposed. But Congress has altered the makeup of the budget some.

(The lawmakers' "reduction" of the fiscal 1979 deficit -- to an estimated $37 billion, from $61 billion proposed by the White House -- stemmed mainly from a smaller tax cut and a shortfall in government spending, not from big cutbacks.)

Moreover, the budget process has become the major political forum for debates over broad economic policy and major spending decisions. Budget resolutions in the House inevitably are narrowly won.

The push toward congressional independence is heightened by the fact that the lawmakers now have their own budget experts -- in the Congressional Budget Office -- to provide economic and budgetary analysis apart from the administration's.

The agency's forecasts and estimates often differ from those of the White House (the CBO is nonpartisan, and is critical of both Democratic and Republican proposals), often providing backing for a congressional-White House split.

Observers say the difference could prove particularly pronounced this year. The CBO is said to be preparing a decidedly less-optimistic economic forecast than Carter's -- altering the budget outlook significantly.

Here's the schedule for the congressional budget process this year:

April 15 -- The House and Senate Budget committees begin work on a new budget resolution for fiscal 1980, which begins Oct. 1, considering recommendations from individual legislative committees that have jurisdiction over specific programs.

May 15 -- The two houses approve a joint resolution establishing informal targets for spending, revenues and the projected size of the deficit. The totals serve as a guide for appropriations committees in the following months.

June through August -- Congress enacts its 14 major appropriations bills for the coming year -- along with any tax-cut legislation -- adhering generally to the targets set earlier. If Congress busts the budget, it must explain why.

Sept. 15 -- The two houses review the money bills they have enacted and decide whether to revise their earlier targets. The second round of targets then becomes a binding spending ceiling, which requires a majority vote to breach.