The Senate approved and sent to the president yesterday an updated mechanism designed to automatically reduce the nation's stubborn budget deficits when Congress and the president don't do so on their own.

The measure, adopted 64 to 34 with bipartisan support, would reinvigorate the 1985 Gramm-Rudman-Hollings balanced-budget law with a new procedure requiring automatic, across-the-board reductions in federal spending if Congress and the White House cannot agree on other means of reaching yearly deficit targets.

The legislation also establishes new annual deficit goals substantially more lenient than those in the 1985 budget law. For example, it delays by two years, until fiscal 1993, the date for achieving a balanced budget.

With Senate passage of the measure, which the House approved Tuesday, Congress has completed the first chapter of this year's budget struggle with the Reagan administration.

It is not known whether Reagan, who previously endorsed the concept of repairing Gramm-Rudman-Hol- lings, will sign a measure that Democratic leaders in Congress have loudly advertised as designed to compel him to accept a tax increase.

"We don't want to signal what the final judgment of the president would be," White House spokesman Marlin Fitzwater said yesterday. Fitzwater, however, reiterated that Reagan has "grave concerns" about "any Gramm-Rudman fix which is designed with the principal purpose of cutting defense or raising taxes."

Frustrated by the administration's reluctance to compromise on spending and tax issues this year, the Democratic congressional leadership backed a Gramm-Rudman-Hollings repair that gives the president a choice of higher taxes or further cuts in the defense buildup -- both of which Reagan opposes.

Like the original law, the amended version would require the automatic spending cuts to be equally divided between domestic and defense programs. The provision in the original law was struck down as unconstitutional by the Supreme Court last year. The new version attempts to fix the constitutional problem by assigning the president's Office of Management and Budget, rather than an arm of Congress, the duty of triggering the spending cuts.

If Reagan vetoes the legislation, said Senate Finance Committee Chairman Lloyd Bentsen (D-Tex.), "He'd put himself in an impossible situation." Bentsen conceded that Congress could probably not override a veto and would have virtually no chance of subsequently passing the tax increase of $10 billion to $15 billion needed under its budget.

Even if Reagan signs the measure, it is unclear how the two chambers of Congress and the White House will agree on the $23 billion in deficit reduction required for the fiscal year that begins Oct. 1. Further sharp disagreements over the size and content of the tax bill and the distribution of spending reductions, particularly in defense, are a near-certainty.

Underlying those debates as the 1988 elections draw nearer will be continued partisan skirmishing over which party is better able to solve the deficit problem and manage the economy.

One possibility is that Reagan would sign the Gramm-Rudman-Hollings bill but veto the tax increase the bill envisions.

"Today's action puts some suspense back in the game," said Sen. Warren B. Rudman (R-N.H.), predicting optimistically that it will "ensure" a summit meeting between the White House and congressional leaders.

Supporters of the measure, attached to legislation raising the federal debt ceiling to $2.8 trillion through May 1989, emphasized that stakes in the continuing struggle to reduce the federal deficit are enormous.

"This has very serious significance for international financial markets," Bentsen said.

Supporters also hailed the bill as a responsible, bipartisan response by Congress to the nation's protracted deficit problems. "We now have a game plan to get the government back in the black," said Sen. Ernest F. Hollings (D-S.C.).

However, the Senate's seven-hour debate underscored Congress' resignation, even sadness, concerning its reliance on an automatic spending-cut mechanism and its retreat from earlier deficit goals.

"We've got to hold a gun to the temple of both the president and Congress," said Senate Majority Leader Robert C. Byrd (D-W.Va.). "I regret we must resort to such a process."

Opponents, led by Sen. Pete V. Domenici (R-N.M.), ranking Republican on the Budget Committee, denounced the measure as fraudulent.

"This particular Gramm-Rudman fix hardly deserves the name," Domenici said. "This is a Trojan horse and nothing more."

The Gramm-Rudman-Hollings revival is supposed to reduce the fiscal 1988 deficit to about $144 billion, $36 billion higher than the comparable goal in the original law. In the following year, the deficit reduction goal is relatively modest, leaving the toughest spending choices until after the 1988 election.