The Senate yesterday began debate on legislation to resurrect the Gramm-Rudman-Hollings balanced-budget law. The body is expected to approve the legislation, but there were predictions that a compromise with the House may not be possible until Congress returns from its August recess.

Senate consideration of the bipartisan measure began late yesterday following a Wednesday agreement between Democrats and Republicans on a new mechanism that requires automatic, across-the-board spending cuts if Congress and the White House fail to meet their annual deficit goals. A final vote is expected today.

The changes in the Gramm-Rudman-Hollings law would also ease the annual deficit targets and delay by one year, to fiscal 1992, the spending period in which the government must achieve a balanced budget. The changes in the automatic spending-cut mechanism are designed to overcome the constitutional objections that prompted the Supreme Court last year to invalidate the law's original mechanism.

"We're saying to the nation -- as loud and clear as we can -- we're serious," said Senate Budget Committee Chairman Lawton Chiles (D-Fla.) as he opened debate on the Gramm-Rudman-Hollings amendment.

But Democratic leaders in the House, who favor a different mechanism they believe would put more political pressure on President Reagan to compromise with Congress on the budget and taxes, criticized the Senate proposal.

"The {Senate} plan needs fixing," House Speaker Jim Wright (D-Tex.) said at his regular news briefing yesterday. "It gives two much unbridled authority to the Office of Management and Budget." The Senate plan gives OMB authority to trigger the automatic spending cuts, although in the first year it is subject to congressional review.

House Majority Leader Thomas S. Foley (D-Wash.) predicted only a "50-50" chance that a compromise can be reached by the time the congressional recess begins the end of next week.

If there is no agreement, Congress would have to adopt another short-term extension of the national debt limit because the Gramm-Rudman-Hollings measure is to be attached to legislation extending the borrowing ceiling until September 1988. Both houses yesterday passed a one-week extension of the debt limit that will give the government borrowing authority through Aug. 6.

The reinvigoration of the balanced-budget law under consideration in the Senate is similar to legislation that easily passed that body last year but died in the House. The amendment gives OMB, rather than the General Accounting Office, the authority to trigger the automatic cuts.

Under the original deficit reduction schedule called for by Gramm-Rudman-Holllings, Congress and the administration were supposed to lower the deficit in fiscal 1988 to $108 billion. But the measure under consideration in the Senate would amend that target to $150 billion, with a $10 billion cushion to account for changes in the economy. The following year, the deficit would have to be reduced by a maximum of $36 billion.

Like the original law, the amendment requires that half the automatic spending reductions come from the Pentagon budget and half from domestic programs if the targets are not met. The amendment makes no changes in the exemptions enjoyed by some politically sensitive domestic accounts, including Social Security, Medicaid and veterans programs.

Within the overall requirement that the military budget bear 50 percent of the mandated cuts, the president would be accorded some flexibility in deciding which Pentagon programs would be affected. However, Congress would have to approve those changes.

Democratic leaders believe that reviving the automatic spending-cut requirement could force Reagan to negotiate a budget compromise with Capitol Hill. Reagan has promised to veto the $19.3 billion tax increase that would provide the bulk of next year's deficit reduction called for in Congress' $1 trillion budget.

If he did, he would face deep automatic cuts in the defense budget. One congressional analysis predicts that Pentagon spending authority could be cut by nearly $28 billion under the automatic cuts.