Democratic and Republican leaders of the Senate said yesterday they will jointly push to strengthen the 1985 Gramm-Rudman-Hollings balanced-budget act and, at the same time, move to ease the law's deficit targets when the Senate takes up legislation next week to raise the federal debt ceiling.

Senate Budget Committee Chairman Lawton Chiles Jr. (D-Fla.) and the panel's ranking minority member, Sen. Pete V. Domenici (R-N.M.) announced yesterday that their party leaders would seek to pass a new version of the law's automatic budget-cutting mechanism that would trigger across-the-board reductions if Congress and the president do not meet their deficit targets. The original automatic "trigger" in Gramm-Rudman-Hollings was declared unconstitutional by the Supreme Court last year.

Under the bipartisan plan, the deficit reduction targets established by Gramm-Rudman-Hollings would also be relaxed. In place of the firm yearly targets now called for in the law, the legislation would aim for annual reductions of about $36 billion. That would make the deficit target for fiscal 1988 more than $135 billion rather than the $108 billion called for now.

The Gramm-Rudman-Hollings changes would be attached to must-pass legislation giving the nation enough new borrowing authority to last through September.

Chiles and Domenici also said they are continuing negotiations to use the debt-limit legislation to push for further budget process reforms, including a possible experiment with two-year appropriations and measures designed to make Congress adhere more closely to its budget goals when it enacts actual spending bills.

Despite bipartisan support for using the leverage of the debt limit extension to enact budget reforms, Democrats, who control the 100th Congress, hope to use the linkage to force President Reagan to acquiesce in a $1 trillion budget for fiscal 1988 that calls for $19.3 billion in new taxes.

Reagan has repeatedly promised to veto the tax legislation needed to implement the Democrats' spending plan and has embarked on a public campaign to discredit the Democratic budget.

Democrats have been scheming for some time to package the tax increase in a manner that will put the maximum amount of political pressure on Reagan.

Restoration of the automatic spending cut mechanism previously endorsed in concept by the president is an integral part of that strategy, because it would present Reagan with an alternative that might be even more distasteful to him than a tax increase. With the new Gramm-Rudman-Hollings "trigger" in place, the president would be faced with budget reductions that would cut deeply into military spending if he does not agree to the tax hike.

Attaching the Gramm-Rudman-Hollings fix to the debt limit is designed to put pressure on both the Congress and the administration to accept the proposal since failure to raise the debt ceiling could lead to an unprecedented U.S. default by the end of this month.

The federal debt ceiling is currently $2.3 trillion, but will automatically be scaled back to $2.1 trillion next Friday. A Treasury Department spokesman said yesterday it is unlikely the nation would have to default on its financial obligations until the end of the month.

Democratic leaders of the House, meanwhile, are still pushing to attach a different version of the Gramm-Rudman-Hollings trigger to a longer extension of the debt limit. The differences are likely to be resolved in a conference committee.