Less than a year after Congress let President Reagan run away with the budget, it is choking on high deficits and wants its budget power back.

Perhaps not since the Nixon era have the executive and legislative branches been engaged in so basic a struggle over their roles and powers, and no one pretends to know how it will all turn out.

They only agree in their different ways that the stakes--for the economy and for their own political survival--are extraordinarily high.

In the textbooks the president drafts the budget, then Congress modifies it, sometimes considerably, to suit its own priorities.

Reagan rewrote that script last year when, riding high in the polls, he so mesmerized Congress with his "economic recovery" program that the lawmakers swallowed it just about whole. They approved a huge tax cut and the first stages of a massive military buildup, producing deficits only partly offset by unprecedented cuts in domestic spending--all almost exactly as Reagan wanted.

But now it is Congress that is moving to rewrite the rules. Aghast at the huge deficits that flow in large part from what they did last year and alarmed that the deficits will keep interest rates at politically and economically dangerous levels, leaders of Reagan's own party in Congress are pushing for an alternative--preferably a "bipartisan alternative."

They deny they are trying to wrest the budget initiative from Reagan, but that is the direction in which they are moving. And for this there is no precise parallel.

Two years ago, Democrats nervous over President Carter's big deficits forced that administration to redraft its budget. But Carter went along, and his people did the actual rewriting. This year, with Reagan refusing to budge so long as Congress had nothing to offer but a mouthful of complaints, the Republicans are forced--as Reagan put it last month--to "put up or shut up."

So far they have put up mostly trial balloons--a whole sky load of them.

Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) suggested an income surtax for defense. Senate Finance Committee Chairman Robert J. Dole (R-Kan.) floated a proposal to scuttle the third year of the tax cut in favor of an early start in indexing tax rates to inflation. In addition to raising some taxes, Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) and the committee's ranking Democrat, Sen. Ernest F. Hollings (S.C.), proposed freezing some domestic spending and reducing the defense spending increase.

Some House Republicans complain that the senators are overdoing it, but there are House GOP options floating around, too.

The balloons were the easy part. The hard part starts this week.

Baker and Domenici spent a good part of last week collecting "options" from the Senate Appropriations, Finance and Budget committees in hopes of fitting them together into a plan, or set of alternatives, for submission to Reagan fairly soon. The chairmen of these committees will meet with Baker starting tomorrow to try to sort out recommendations.

Baker is reportedly aiming to have a set of proposals ready this week, but Dole, whose committee faces the most difficult choices in dealing with taxes and basic benefit programs like Social Security and welfare, says it will probably take longer. Even getting agreement from the leaders may be more difficult than Baker's timetable suggests, some insiders are saying.

If the leaders can agree and if Reagan goes along, or at least agrees to negotiate a compromise, the Republican-controlled Senate might well fall in line with a huge sigh of relief.

But the Democratic House is another matter. Democrats there are talking compromise, but will they agree to freeze Social Security benefits, for instance, if that is part of the final plan? Moreover, is there any political profit for them in bailing out the Republicans in an election year?

If Reagan refuses to go along, or simply leaves Congress dangling by an ambiguity, the outlook gets even bleaker.

Domenici and others say Reagan's budget, with its high deficits despite controversial spending cuts, simply won't be approved by Congress. Baker says no other budget will pass "unless he Reagan at least acquiesces in it." Many Democrats agree, saying they don't want to be part of a bipartisan budget coup if Reagan turns around and tries to make them the scapegoats for a worsening of the economy.

At the risk of angering his fellow Republicans even more than he already had, Reagan last week exempted Republicans from his almost drumbeat criticism of congressional budget writers, but he showed no other outward signs of conciliation as he continued to defend his budget against all other proposed alternatives. It is an open question whether he will compromise after seeing the senators' proposals.

In terms of strategy, Reagan could have Congress over a barrel if, as some suggest, he is counting on an economic upturn, with falling interest rates, to take the steam out of the budget rebellion sometime this spring. If, by failing to bless a budget alternative, he prevents a bipartisan consensus from emerging in the meantime for something else, his budget might well be the only budget on the table. Domenici might churn something out of the Budget Committee, but what about Baker's reluctance to defy Reagan, and the Democrats' refusal to play fall guy?

The real test would then come in May, when a debt ceiling extension has to be passed to keep the government operating. There is almost universal agreement that neither the budget nor the debt bill will be passed without inclusion of substantial deficit reductions. Reagan demonstrated forcefully last year that he didn't mind shutting down the government for a while to get his way. Congress might have to be prepared for a more protracted shutdown this time if it wants to hang tough.

Reagan has his own set of deficit reductions, but committee after committee signaled last week that they didn't like them, especially those aimed at programs that were heavily cut last year. This means the deficit could go even higher than the $91.5 billion that Reagan projects (and which the Congressional Budget Office says is really more like $121 billion even with Reagan's savings).

These early warning signs of trouble were one reason for the rush to come up with a plan. Members complain they need some guidelines--if not Reagan's budget, then what? "There is a fear things could really get out of control," said a Senate Republican leadership aide.

Others say things may already be at that point.

Rep. Leon E. Panetta (D-Calif.), whose budget expertise is respected by colleagues in both parties, paints a grim picture of stalemate broken only by disaster.

So long as the economy "just slops along" as it's doing now, said Panetta the other day, there is little chance of the two parties overcoming their differences and compromising on what amounts to very important programs and policies.

Moreover, not since Watergate has such a Congress attempted such a takeover of major executive responsibilities. "For Congress to take the ball away from the administration and run with it, it would take something pretty dramatic," he said.

Like what, he was asked. A sharp decline in the stock market, a whole string of savings and loan failures and the collapse of a major corporation would probably get Congress' attention, he answered. "Then you'd see something pretty quick."