The Senate broke another bitter impasse over arms control last night after Democrats threatened to hold up confirmation hearings on Supreme Court nominee Robert H. Bork and keep the Senate in round-the-clock session to force filibustering Republicans to abandon their stalling tactics.

Only a few days after the Senate appeared to have broken a stalemate holding up defense and arms control legislation, partisan strife broke out anew, threatening a rancorous fight just as President Reagan was meeting with Soviet Foreign Minister Eduard Shevardnadze on a new arms pact.

Senate leaders finally resolved the latest dispute by agreeing to vote on competing Democratic and Republican resolutions dealing with the Senate's role in treaty-making. Under the agreement, the Senate today will begin to confront the key issue: a Democratic proposal to require congressional approval before the Reagan administration could reinterpret the 1972 Antiballistic Missile (ABM) Treaty to allow expanded Strategic Defense Initiative, or "Star Wars," testing and development.

In a late-night roll call, Republicans joined in passing the Democratic-sponsored resolution, which affirmed the Senate's role in treaty-making.

The Democratic proposal, which supported Reagan's negotiating efforts while reserving judgment on treaty provisions until they can be given "thorough examination" by the Senate, was approved, 92 to 1, with Sen. Jesse Helms (R-N.C.) in lone dissent.

The Republican proposal, which would have put the Senate on record against trying to legislate on the ABM issue during the current U.S.-Soviet negotiations, was then rejected, 59 to 35.

During the debate, which was punctuated by threats of "going to the mattresses" for all-night sessions extending through the weekend, Republicans accused Democrats of "heavy-handed" tactics; Senate Majority Leader Robert C. Byrd (D-W.Va.) declared angrily: "I've had my fill of being jerked around by the {GOP} minority." At another point, Byrd told the Republicans that if they were going to filibuster, they would have to "do it the old-fashioned way," staying all night "and earning it."

Senate Armed Services Committee Chairman Sam Nunn (D-Ga.) put the Senate on notice that he would object to holding any committee sessions so long as the Republicans continued to filibuster, which would have cut off today's Bork hearings after only two hours.

"Who's being obstructionist now?" asked Minority Whip Alan K. Simpson (R-Wyo.), in reference to earlier Democratic charges that the Republicans were being obstructionist in holding up Senate action on a variety of Democratic initiatives.

"I'll tell the senator. I am," retorted Nunn angrily.

In backing the Democratic proposal, Nunn ridiculed the Republican language, saying it was tantamount to having "the Senate of the United States declare itself a potted plant . . . an ornament in the foreign policy arena, adorning but having no influence."

Noting the division of powers in the Constitution, Nunn said Americans "didn't want King George III or King Ronald XVI."

Republicans countered with the argument that Democrats were proposing to intrude unconstitutionally on the president's treaty-making powers.