Senate Republicans, reinforced by top Reagan administration officials, yesterday thwarted a Democratic attempt at a showdown over controversial arms-control proposals that have stalled action on the $300 billion defense authorization bill for fiscal 1988.

After the Democrats failed in their latest attempt to revive the defense bill, Armed Services Committee Chairman Sam Nunn (D-Ga.) served notice that he will try to reach an informal agreement with the House on the measure if the impasse is not resolved before Congress begins a four-week recess Aug. 8.

In the absence of Senate action, Nunn said, he will seek agreement between the House and Senate Armed Services committees that could serve as "advice" to both chambers' Appropriations committees in drafting a defense spending bill for fiscal 1988.

This would mean no defense authorization bill for next year, which could complicate some Pentagon programs, even though most could be handled in the spending bill, according to congressional experts.

It would also virtually assure a showdown over arms control in connection with an omnibus spending bill that Congress will have to pass by Oct. 1 to fund the government for the new fiscal year, adding one more contentious issue to a bill expected to involve everything from social-welfare spending to aid for the Nicaraguan contras.

While the Democrats could use the leverage of fiscal crisis to force a vote on the arms provisions, Republicans said yesterday that a delay would work to the administration's advantage as U.S.-Soviet arms negotiations move toward a possible summit between President Reagan and Soviet leader Mikhail Gorbachev. Democratic arms-control efforts last year were derailed when the administration argued on the eve of the Iceland summit that congressional arms limitations would undermine Reagan's position in dealing with Gorbachev.

The immediate flash point over arms control in the Senate is a Nunn-sponsored provision of the defense bill that would prevent the administration from going beyond a narrow interpretation of the 1972 Antiballistic Missile (ABM) Treaty in developing the president's Strategic Defense Initiative (SDI).

But a House-passed version of the defense measure also includes other arms constraints, including a provision to force the United States back into compliance with the unratified SALT II treaty and to ban all but the smallest nuclear tests so long as the Soviets refrain from testing. The SALT II provision is considered to have more support in the Senate than the test ban, perhaps enough for enactment.

The Reagan administration is adamantly opposed to all these provisions. When Senate Republicans met yesterday to consider the new Democratic move, Defense Secretary Caspar W. Weinberger and national security adviser Frank C. Carlucci reportedly agreed with the GOP lawmakers that the arms-control provisions were unacceptable as part of the defense bill.

"They {administration officials} don't want a defense bill loaded down with arms-control provisions," said Sen. Dan Quayle (R-Ind.) after the meeting. He said Senate Republicans also held firm on the issue. "We're just not going to put the president in the position of negotiating more with Congress than with the Soviets," he added.

Republicans suggested instead that the ABM, SALT II and related issues be considered in connection with a pending State Department authorization bill. Democrats rejected the proposal, in part because they have linked it to SDI spending in the defense bill, a linkage they would lose if arms-control provisions were shunted off to another piece of legislation.