Senate Democrats called unanimously on President Reagan yesterday to rewrite his budget and consider deferring both the scheduled 1983 individual tax cut and future indexation to keep taxes from rising with inflation.

The proposal came only a day after Reagan dug in against any change in his tax cut program, characterizing his budget critics as would-be tax-raisers.

Though the Democrats said they were just trying to avoid a political deadlock, they also injected a new note of partisanship into the budget battle just as Senate Republican leaders met for the first time with senior Democrats on fiscal committees to start assembling a bipartisan alternative to Reagan's high-deficit spending plan.

While the Democrats called on Reagan to "submit a new fiscal year 1983 budget incorporating lower deficits and a commitment to a balanced budget," they committed themselves to nothing aside from considering whatever Reagan might recommend. And several ruled out cuts that some members have proposed in cost-of-living increases for Social Security and indicated misgivings about other social program reductions.

Senate Republicans appeared no closer to specific alternatives either.

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) laid out a dozen or more spending cut options at a meeting of all Senate Republicans, but no recommendations were made and no consensus was reached on anything, sources said. Tax increases were not even discussed. "We were indoctrinated on the severity of the problem," said Sen. Dan Quayle (R-Ind.).

While Republicans and Democrats alike were dancing gingerly around the hard choices that Congress faces in trying to reduce deficits, Wall Street analyst Henry Kaufman plunged right in, urging specific measures to reduce Reagan's projected deficit by at least half.

Warning that "our economy and financial markets are more fragile than at any time since the end of World War II," Kaufman urged Congress to overhaul Reagan's budget by scuttling most of his individual tax cuts and canceling cost-of-living increases for major benefit programs.

Major budget surgery, along with reforms in the Federal Reserve's monetary policies, are needed to prevent a collapse of the expected economic recovery later this year and even "greater economic risks" in the future, Kaufman warned the House Budget Committee.

Kaufman challenged the economic assumptions under which Reagan projects a deficit of less than $100 billion for next year, suggesting the figure will probably be more like $135 billion.

Unless Congress is willing to make deep cuts in Reagan's big military buildup, he said, it should offset the costs by reducing this summer's scheduled tax cut from 10 percent to 5 percent and eliminating the 10 percent tax cut scheduled for 1983. But even with those revenue increases and with canceling inflation adjustments for spending programs, more savings will be needed to reach "a more acceptable deficit range of $50 billion to $70 billion," Kaufman asserted.

For the future, he said, Congress should consider abandoning all inflation adjustments, for both spending and taxes, to help "create constituencies that are opposed to inflation." He also proposed an end to "double taxation" of dividends and capital gains and "gradual replacement of part of the current income tax structure with consumption-oriented taxes," which he said should be aimed at discretionary spending.

The Senate Democrats' appeal to Reagan was adopted without dissent at a caucus attended by 41 of its 47 members, according to caucus aides, and incorporated into a letter to Reagan from Senate Minority Leader Robert C. Byrd (D-W.Va.).

Byrd later told reporters the move was aimed at "intensifying the bipartisan effort . . . to end the budget paralysis in which we find ourselves." But at the same time he accused Reagan of having "stonewalled during six precious weeks of economic deterioration."

Asked what spending cuts the Democrats would accept in exchange for a Reagan retreat on taxes, Byrd mentioned only defense, which Reagan has refused to cut. As for anything else, Byrd said, "Let's see what he recommends."

On the controversial issue of canceling or modifying cost-of-living increases for Social Security and other benefit programs, which Republicans are studying as an option, Byrd said there would be "few votes on the Democratic side" even if Reagan proposed it.

House Speaker Thomas P. O'Neill Jr. (D-Mass.) said yesterday House Democrats would look at such a proposal only if Reagan embraced it. O'Neill did not reject the idea out of hand as he has before. But the White House appeared to rule it out over the weekend, which annoyed some Senate Republicans.

Meanwhile, the House Appropriations housing subcommittee rejected most of Reagan's proposal for $9.4 billion in housing rescissions, agreeing to only $100 million in rescissions but saving another $3.8 billion by deferring spending to next year. It retained the 24,000 new housing units that Congress approved last year and Reagan wanted reduced to 310.