House Minority Leader Robert H. Michel (R-Ill.) yesterday laid out in the greatest detail so far the emerging budget strategy of the Republican leadership in Congress, which is to send President Reagan a rewritten version of his budget as part of a bill to raise the debt ceiling later this spring.

Michel told reporters that an increase in the debt ceiling that the administration will need by May cannot pass the House unless it is linked to "a budget resolution that indicates we are narrowing the deficit somewhat" below the $91.5 billion the president has forecast for fiscal 1983.

He said the way to do that, in his judgment, would be to trim the president's planned defense increases, reduce cost-of-living increases in benefits under the various federal entitlement programs and defer the final round of the Reagan tax cut, scheduled for July 1, 1983.

Those suggestions paralleled proposals put forward in recent days by leading Republicans in the Senate, including Budget Committee Chairman Pete V. Domenici (R-N.M.), Finance Committee Chairman Robert J. Dole (R-Kan.) and Majority Leader Howard H. Baker Jr. (R-Tenn.).

But Michel went beyond what they have said, in also advocating repeal of the tax-indexing provision that is supposed to take effect in 1984, and adjust tax rates automatically every year to keep taxpayers from being pushed into higher brackets by inflation.

Michel said he had told the president, "I would be willing just to wipe that indexing provision out." He said Reagan had not advocated indexing "in the first place," but he conceded that the president "didn't leap to the bait" of writing off a provision he heartily endorsed when it became part of the 1981 tax bill.

Michel said, however, that he was not looking for approval from Reagan at this time, just room to negotiate.

The Republican leader told reporters he had begun discussions with House Democrats, including Budget Committee Chairman James R. Jones (D-Okla.) and Majority Leader James C. Wright Jr. (D-Tex.). And despite election-year pressures and the bruises of last year's budget fights, Michel said he was encouraged about the prospects for a bipartisan budget and debt-ceiling bill.

"But I haven't talked to the Godfather yet," he said, referring to House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.).

And Michel conceded that some Democrats are suspicious that Reagan may let them take the political risk of voting to trim entitlements and roll back promised tax cuts only to veto their product or go to the voters and complain that Congress aborted his economic program before it had a chance to succeed.

Yet Michel rejected suggestions that Reagan give his blessing in advance to the efforts to rewrite his budget. "The president can't be in a compromising position at this time," Michel said. "There are too many things proposals floating around. If he moves, he just muddies the waters."

Senate leaders have been proposing alternatives to the Reagan budget partly as signals to the president that it will have to be changed. Some White House officials have spoken approvingly of the efforts of these senators to trim the likely deficit, but always with the proviso that Reagan does not want the planned defense increases trimmed or the promised tax cuts delayed.

But a participant in the recent Camp David political strategy meeting of White House aides and political advisers said yesterday, "I don't know of anyone on the White House staff that isn't praying that Congress does their work for them."

Without endorsing specific figures, Michel said, "I'm not going to be surprised" if defense increases are scaled back and entitlement boosts trimmed.

He was unusually blunt in describing the political and economic need for rewriting the Reagan budget. Speaking of the supply-side theory of economics underlying the three-year, 25 percent tax cut, he said, "Everyone's expectations were grossly exaggerated, especially on the timing . . . . This great big thing the economy doesn't turn on a dime. It's not the Reagan revolution. It's got to be an evolution over time."

Michel said the first 5 percent individual income tax cut last October "didn't do a darn thing to stimulate" the economy, and he suggested the 10 percent cut scheduled for this July might be more effective if it were made retroactive to the start of this year.

If it were speeded up, he said, and the economy responded, then he would be willing to defer the last 10 percent of the tax cut scheduled for mid-1983 and repeal indexing, in order to assuage the investment community's fears about overwhelming deficits extending into the indefinite future.

Michel conceded that he was eager to advance the 1982 tax cut and speed work on the budget because of his concerns about Republican chances in the November election. He said that a September or October recovery would come too late to help Republicans, because of the "perception lag" in the press.

For that reason, he said, he and Baker had rejected White House talk of slowing action on the budget in hopes of a better economic climate this spring and summer.

He said he hoped the Republican Senate would agree on an alternative budget proposal before the Easter recess, and pass it in time for the House to consider it as part of the debt-ceiling bill the administration is expected to need by May when deficits push to the current $1 trillion level.

Michel and Republican members of the House Ways and Means Committee met with the president yesterday afternoon, but they told reporters that they discussed only the modest tax changes Reagan proposed as part of his budget, not overall budget strategy.