The Senate yesterday broke a two-week deadlock over the MX missile as Democratic presidential hopeful Sen. Gary Hart (D-Colo.), saying that he had stimulated public debate over the controversial nuclear weapon, joined Republican leaders in agreeing to a vote on the issue Tuesday.

While not contesting MX proponents' claim that the GOP-controlled Senate would authorize $4.6 billion for the MX, including $2.5 billion for production of the first 27 missiles, Hart said anti-MX senators will continue their fight in appropriations votes later this year.

"This will not be the last we will hear of the MX . . . . I think you will see the debate intensifying instead of diminishing," Hart told reporters after Majority Leader Howard H. Baker Jr. (R-Tenn.) announced the voting schedule and abandoned plans to continue seeking cloture votes to choke off Hart's quasi-filibuster against the weapon.

Armed Services Committee Chairman John G. Tower (R-Tex.) later disclosed that the Republican leadership would have lost a cloture vote yesterday because of absentees but claimed it would have had the votes to win on Monday.

A GOP leadership aide characterized the two-week stall, in which Hart and other MX foes tried to build the case against the weapon as an invitation to escalation of the arms race, as a "draw."

A final vote on the MX will clear the way for the Senate to pass its $200 billion defense authorization bill for next year, probably before the House completes work on its version of the measure.

Earlier this week, the Democratic-controlled House voted 220 to 207 to approve production funds for the MX but later attached some strings, including limiting the number of missiles the Pentagon can buy next fiscal year and linking their deployment to administration progress on arms control.

Under the Senate's voting schedule, Hart and his allies can obtain votes on up to four MX-related amendments, including one to stop production of the missile as well as others to link its production to arms control progress. Another amendment would ban the MX and urge development of a smaller, less-threatening alternative called Midgetman.

The painstaking negotiations that led to the procedural agreement--which went so far as to require personal initialing of specific provisions--underscored the tensions and barely contained bitterness of the debate, even though the Senate never reached a full-scale confrontation over the merits of the missile.

Republicans accused Hart privately of staging the fight to bolster his sagging presidential campaign, suggesting that he was planning to use it as fund-raising fodder, and Democrats complained that Tower used heavy-handed, sneaky parliamentary tactics to prevent a real debate.

Tower yesterday denied that he attempted to thwart debate, contending that "We stated our case completely." Hart disagreed, saying, "We haven't gotten the other side to defend the missile . . . . I think that speaks volumes."

Late Thursday, as Republicans resisted Democrats' attempts to draw them into debate, MX opponents staged a discussion among themselves aimed that demonstrating that the huge new intercontinental ballistic missile, which would be housed in existing Minuteman missile silos, is so vulnerable to attack that it has become, in effect, a first-strike instead of defensive weapon.

Calling its first-strike potential a "prescription for annihilation," Sen. Joseph R. Biden Jr. (D-Del.) accused the administration of an "instinct for nuclear madness" and said it was getting on a "treadmill" that could lead only to disaster.

Accusing the administration of being "macho" in its approach to arms control, Sen. Dale Bumpers (D-Ark.) observed caustically: "I don't think it's our macho that's on the line, it's our sanity."

When the Senate last voted on the MX issue, it approved flight-testing for the missile and initial expenditures for basing by a 59-to-39 vote. "There could be a little slippage, but not enough to change the outcome," Tower said yesterday.

Said Hart: "I'm an eternal optimist."

In other action on the defense bill as a whole, the Senate late Thursday approved an amendment by Sens. Carl Levin (D-Mich.) and William S. Cohen (R-Maine) to require the Pentagon to establish maximum in- creases for prices of spare parts for military equipment. A contracting officer would have to certify that a further price increase was "fair and reasonable" before the ceiling could be breached.

Aides said the Levin-Cohen proposal was a response to recent reports of major increases in the price of military spare parts, including a draft report by the Pentagon's in- spector general showing that the cost of nearly one-third of approximately 15,000 spare parts had increased five-fold from 1980 to 1982.

The proposal, which would require the Pentagon to establish the new regulations within 120 days of the bill's passage and submit them for clearance by the Armed Services committees, was accepted by Tower and approved without dissent.