Putting aside claims that a congressional budget is the key to lower interest rates and economic recovery, Republican leaders said Friday that expected final passage of a budget next week is unlikely to have any immediate lasting effect on either the economy or financial markets.

"I think it's been overemphasized as to how much we, in what we're doing here on the budget thing, influence the money markets up there," said House Minority Leader Robert H. Michel (R-Ill.) in attempting to explain why interest rates rose and the stock market fell just as House-Senate conferees were wrapping up a budget compromise on Thursday.

Moreover, the budget will only have an impact "if it is implemented and if the markets believe it or can be led to believe it in the near future," said Senate Budget Committee Chairman Pete V. Domenici (R-N.M.), who joined Michel in anticipating it will be passed by both houses next week.

In a day of muted expectations following the conferees' approval of a fiscal 1983 budget with a record deficit "target" of $103.9 billion, which many members say will probably turn into a real deficit of $120 billion to $130 billion, attention turned to what what is expected to be the even more difficult task of conforming to the budget's requirements of tax increases and spending restraint.

Not only must congressional committees attempt to come up with $21 billion in tax increases and a downpayment of nearly $7 billion in program cuts for the next fiscal year, many of them in popular benefit programs, but they must defy all the political rules and do so within about 100 days of election day.

At the same time that this so-called "reconciliation" process is under way, the appropriations committees will be trying to crank out money bills under the terms of the budget resolution, requiring that they virtually freeze spending in most categories. These terms are reinforced by a rule that no money bill can be enacted if it exceeds budget targets.

Draconian as this may sound, Congress is the political equivalent of an 800-pound gorilla; it can do anything it wants, including busting right through the chains it puts on itself.

Fear that it may eventually do so, especially as self-discipline fades with the approaching November elections, is one reason why few on Capitol Hill will be surprised if Wall Street doesn't throw a ticker-tape parade for final passage of the budget.

At least privately, they acknowledge that the budget, despite all the rhetoric about its importance from both ends of Pennsylvania Avenue, means little unless legislation is passed to enforce it. And powerful forces, from high-powered Washington lobbyists to folks back home who don't want their favorite programs cut, are working to seek that the legislation isn't passed.

What worried Domenici, he told reporters Friday, was that he was hearing comments to the effect that "We'll vote this budget in and then not do those things that are prescribed" in it. Wall Street will be looking at the enforcement, he said. "That is the issue."

Michel suggested that economic revival hinges more on forces outside Congress, such as manufacturing, than on what Congress might do. "What we're doing here, if we have any influence at all, can't be anything but a good sign," he said, adding, however, that "it goes beyond what we do here."

As Domenici noted, the budget that the conferees approved after a marathon session early today calls for an extraordinary $378 billion in deficit reductions over the next three years, including $98 billion in tax increases and the rest in spending retrenchment, mostly on the domestic side.

But the spending cuts are not even all mandated through "reconciliation." Nearly $14 billion of the 1983 savings, for instance, are so-called "management savings" for the administration to make.

Cuts in the administration's huge military buildup program amount to $26.3 billion by 1985.

Domestic appropriations would be largely frozen for next year, saving $6.3 billion, and benefit entitlement programs--with the conspicuous exception of Social Security--would be cut back by $6.4 billion, including savings from limiting cost-of-living increases for many programs to 4 percent. Federal pay boosts would also be limited to 4 percent.

Programs like legal services for the poor, subsidized housing and postal rate subsidies were saved, but with cutbacks. Some agencies with controversial duties, like the Federal Trade Commission, were targeted for heavy cuts, with the FTC cut nearly one-quarter below what even the administration wanted.

Among entitlement programs, the biggest single cut would be in Medicare followed by food stamps and child nutrition at $900 million, Medicaid at $700 million, welfare (including Supplemental Security Income) at $590 million and subsidized housing at $250 million.

For the first time, government credit programs would be put under budget restraints, but congressional leaders said the projected ceilings were so high that they would have little effect.

In many cases, spending cuts represented modifications of even deeper slashes approved when, for the second year in a row, the House defied its Democratic leadership and approved a budget tailored to President Reagan's conservative agenda for the government.

But, generally, the conferees' compromise was patterned after the House version of the budget, largely because of fears that the House might balk at any major deviations.