Congressional Democrats and Republicans on key financial committees said yesterday that President Reagan must become involved personally in the search for a budget compromise or risk huge federal deficits for the foreseeable future.

Robert J. Dole (R-Kan.), chairman of the influential tax-writing Finance Committee, said, "It's time for the president to become a participant in the budget process."

Speaking on "This Week With David Brinkley" (ABC, WJLA), Dole warned that without a congressional budget resolution for fiscal 1984, which will begin Oct. 1, large deficits could lead to "some danger of the economy sort of sputtering out."

House Budget Committee member Richard A. Gephardt (D-Mo.) said on "Meet the Press" (NBC, WRC) that a budget compromise that would reduce the huge deficits projected for later years would be possible "if, and only if, we can get the president engaged in the budget process."

Fellow Budget Committee member Timothy E. Wirth (D-Colo.), appearing with Gephardt, said it is "absolutely imperative" that the Senate pass a budget resolution and go to conference with the House. "And that means the president must become involved," he added.

Dole and other Senate Republican leaders met with White House aides Friday after efforts to pass a Senate budget resolution collapsed.

The Senate has been unable to muster a majority for any budget plan, with disagreement centering on how much to spend on defense next year and whether to raise taxes significantly to help close the budget gap.

White House aides said Friday that the president will give the Senate leadership "running room" to fashion a budget resolution that can command a majority.

The House has passed a resolution allowing a 5 percent increase in defense spending, after inflation, and $30 billion in tax increases in fiscal 1984.

Reagan's personal arm-twisting has been credited for many of the administration's fiscal victories in 1981 and 1982.

But this year, despite deficits soaring towards $200 billion, the president has not taken as prominent a role.

While he has threatened to veto major tax increases, he has not collared legislators on behalf of domestic spending cuts and has said less in public about the dangers of big deficits.

Asked yesterday on his return from a weekend at Camp David, Md., whether he would become more active in the budget process, Reagan responded, "We'll see you Tuesday night," when he is to hold a formal news conference, the 17th of the president's term and first since Feb. 16.

Dole said yesterday that he still believes "there are enough Democrats and Republicans to put together a fairly conservative budget resolution, but we haven't attempted that . . . .

"That's why I think the president, or I hope the president might indicate he'd like to be a party to the budget process, even though it's a congressional discipline. It's not a spectator sport," Dole added.

Economist Henry Kaufman of Salomon Brothers in New York said on "Face the Nation" (CBS, WDVM) that large deficits are one factor keeping interest rates high and predicted that the rates will not drop much further in coming months and may rise again in 1984.

"I personally feel that we have seen most of the interest-rate decline that we should expect for the time being . . . . I believe that the American economic recovery will continue in a kind of subnormal fashion," Kaufman said.

He credited the Federal Reserve Board and its chairman, Paul A. Volcker, for reducing inflation and said that Volcker deserves to be reapppointed. (White House aides have hinted that Reagan may prefer to appoint someone else when Volcker's term expires this summer.)

Two economists who appeared on the Brinkley program, Lester Thurow and Arthur Laffer, agreed with Finance Committee Chairman Dole that tax increases would be harmful to the economic recovery.