President Reagan's fantastic economic flying machine ran into some rough weather on Capitol Hill last week, clouding the outlook for his controversial three-year, 30 percent, across-the-board income-tax cut proposal.

Only two weeks after its stunning victory on the budget resolution, the White House is finding itself on the defensive over the tax-cut package. The hoped-for spillover of support to the tax plan simply hasn't come about.

The buffeting stems from several crosscurrents:

First, Reagan's untraditional Kemp-Roth tax-cut plan has roused too many skeptics to pass intact. Conservative Democrats, who bolted to support Reagan's budget cuts, aren't biting at this one. Even many Republicans are leery.

Second, as Reagan is discovering, the tax-cut fever on Capitol Hill isn't nearly as high as the fever for budget-cutting, mirroring the wariness of Wall Street traders and many voters, who fear a big deficit would spur inflation.

Finally, the package is being threatened by the prospect that House and Senate tax-writers may draft a bipartisan compromise of their own, a move that would speed action on the bill but ultimately reduce White House influence.

As a result, there now seems only an outside chance that the administration could forge the same kind of Dixie-GOP coalition on the tax bill tha provided that margin for the president's spectacular victory on the budget.

Indeed, for all its earlier tough talk about opposing any compromise on the tax bill, the administration already is backing off a bit in recognition of the political realities.

Treasury Secretary Donald T. Regan has begun sounding out key congressional figures on postponing the reduction for individuals to October, instead of this coming July, and paring the three-year cut to 25 percent from 30 percent.

In return, Regan has hinted the administration would be willing to accept some of the tax-cut proposals that have been proffered by Democrats, slashing the top rate to 50 percent from 70 percent and trimming the marriage penalty.

If the compromise were successful, it could help speed the tax-package through the two houses before Congress' August recess. It also would trim the fiscal 1981 and 1982 budget deficits, which are troubling the bond markets.

To be sure, as all parties caution, any real compromise is still a good bit away. All that's happened so far is that the various players have agreed to talk turkey. There's still no agreement on the Oct. 1 plan or any other.

Rep. Dan Rostenkowski (D-Ill.), chairman of the House Ways and Means Committee, still hasn't abandoned his own push for a single-year tax cut rather than the three-year reduction that Reagan wants.

Rostenkowski also wants the tax cuts targeted more toward lower- and middle-income groups than the president's proposals. And Democrats on the Senate Finance Committee have a spate of their own pet proposals to tack on.

Any more toward a compromise will be laborious. Rostenkowski first must consult with key House Democrats to see what his own comittee -- and the Democratic leadership -- will buy.

Then comes a round of negotiations with Senate Finance Committee chairman Bob Dole (R-Kan.) and the ranking minority members of the House and Senate tax-writing panels.

And all throughout, there will be the talks with the administration. (Rostenkowski also must keep the conservative Democrats happy. Although the southerners have vowed to work with him, there's still a chance they'll bolt.)

Just the same, for all the progress on the procedural front, the administration still is playing with a diminished hand.

To the extent that the compromise must win approval from both Dole and Rostenkowski at once, it will mean less influence for the administration and a greater probability that more of Reagan's plan will be pared.

Neither Dole nor Rostenkowski -- nor their panels' ranking minority members, Sen. Russell B. Long (D-La.) and Rep. Barber B. Conable (R-N.Y.) -- has much love for Reagan's three-year across-the-board cuts.

If anything, the two chairmen share one overriding goal that isn't likely to work in favor of the administration's: Both want to get the tax bill passed quickly and smoothly, without risking a free-for-all on the floor.

On paper, a workable compromise isn't that difficult to put together. On most components, the various actors aren't that far apart. All want faster depreciation writeoffs for business. And all want some personal cuts.

Moreoever, even the Democrats this time seem largely agreed among themselves. Rostenkowski's own plan, for example, is virtually a clone of the tax bill drafted last summer by the Senate Finance Committee.

But nailing the compromise down in fact doubtless will be more difficult than merely laying out its elements abstractly. What congressional negotiators have to do is to decide how much they need to pare Reagan's proposed across-the-board tax-rate cuts in order to fit in the Democrats' pet proposals:

Slashing the top tax rate on investment income to 50 percent, from 70 percent now, reducing the so-called marriage penalty, cutting estate and gift taxes and increasing existing incentives for retirement savings.

There's another secondary, but politically important, shopping list: Dole wants to cut the 1980 crude-oil tax for royalty owners. Long wants incentives to spur employe stock ownership plans. Others want research and development credits.

Most of these proposals already have the support of the administration, but the White House wants them put off until a second tax bill, to be proposed in August, so as to leave more room for Reagan's full 30 percent cut.

The question now is, will the administration agree to trim back its own plan to make room for the others in a single bill? Most lawmakers, understandably, are skeptical that Congress will have time for a second bill.

For the moment, the outlook still is fuzzy. As Conable put it late last week, there's been progress on procedure, but nothing on substance. Both sides have ended their initial cat-and-mouse game. Now the bargaining can begin.

In a broad sense, the administration almost can't lose -- and already may have won the fight. There's no argument over whether to cut taxes, and its business tax proposal seems well in hand.

Even if Reagan gets only part of his plan, the bill still would be a big departure from traditional Democratic tax-cuts. And Rostenkowski, fearful of suffering a floor defeat such as that on the budget, has reason to give ground.

But politically the situation still is a far cry from Reagan's upper hand on the budget fight, where the administration seemed to be calling all the bids and winning smashingly on every play.