The MX missile cleared its first "make-or-break" hurdle in Congress yesterday as the Senate, in a major victory for President Reagan, voted 55 to 45 to continue production of the controversial nuclear weapon.

The margin in the Republican-controlled Senate was wider than had been predicted by either side of the intense MX battle, giving Reagan the upper hand in next week's showdown in the Democratic-led House.

The vote showed increased support for the MX since the Senate split 48 to 48 on the issue last June, when Vice President Bush was forced to cast a tie-breaking vote to save the weapon. Several senators, however, said they have misgivings about voting later this year for 48 more MX missiles.

"There were an awful lot of people out there holding their nose," said Sen. Gary Hart (D-Colo.), a leading opponent of the MX.

The president hailed the vote as "a message of American resolve to the world."

Yesterday's vote followed a heavy lobbying campaign by the White House, including a personal appeal from Reagan during a Capitol Hill luncheon with Republican senators only hours before the vote.

Senators on both sides of the issue attributed the outcome largely to Reagan's warning that defeat of the MX would undermine the U.S. bargaining position in the current arms control talks with the Soviet Union in Geneva.

Reagan made his final appeal to the Senate yesterday to support the MX "in the name of peace."

In a largely partisan vote, Senate Minority Leader Robert C. Byrd (D-W.Va.) and several Republican moderates were among 45 Republicans and 10 Democrats who voted for continued production. Thirty-seven Democrats and eight Republicans opposed it.

Among Washington-area senators, only Paul S. Sarbanes (D-Md.) opposed the MX.

Sen. Charles McC. Mathias Jr. (R-Md.) was one of seven senators who switched to vote in favor of the MX after voting last year against continued production. The others were Republicans Gordon J. Humphrey (N.H.), Bob Packwood (Ore.) and Arlen Specter (Pa.) and Democrats Lloyd Bentsen (Tex.), David Boren (Okla.) and Russell B. Long (La.). Only Sen. Nancy Landon Kassebaum (R-Kan.) switched from support to opposition.

Reagan lobbied Mathias and a few others until shortly before the vote, meeting privately with Mathias at the White House yesterday morning and giving him a ride back to the Capitol when Reagan went to meet with the Republican senators.

In yesterday's vote, which both sides agreed was a critical test for the MX, the Senate authorized release of $1.5 billion for 21 new missiles. The funds had been appropriated but frozen last year.

It has to vote again, probably today, on appropriating the money, but the outcome is not expected to change.

The House will have the same two votes next week. MX foes conceded that the unexpectedly strong Senate vote for the MX could have a "substantial effect" on the House, which a tally by anti-MX forces shows almost evenly split, with 24 members undecided. "It the Senate vote makes it easier for people to switch," said a House Democratic leadership aide.

Although the MX could be scuttled in any one of the four votes, both the White House and the missile's opponents agreed that the first Senate vote was the critical one. Even though the Senate is controlled by Republicans, it had been considered by many as the least friendly turf for the missile this year.

However, opponents contended that the Senate is more amenable to White House pressure than is the House and argued that a House reversal is possible.

"I think it's winnable in the House," although it will be "tough," said Hart.

Although the Senate galleries were packed for the vote, with Bush again in the chair in case of a tie, the vote was anti-climactic because many of the swing senators, including Byrd, had already declared their support for continued production. None of those in serious doubt voted against the missile.

But even many of the senators who voted for the MX, including Mathias, indicated that they have strong misgivings about Reagan's proposal for production of another 48 missiles next year at a cost of $3.2 billion.

Several predicted that the request will be denied or scaled back drastically when it comes up as part of fiscal 1986 defense-spending measures later this year.

Twenty-one missiles are currently in production; approval of the additional 21 would bring the total to just short of half the 100 deployed missiles that Reagan has requested. Some influential lawmakers are talking about halting deployment at about 50.

In daylong debate, both on the floor and off, Democrats focused on the missile and its basing system, while Reagan concentrated on the vote's impact on the arms control talks and some of his allies talked of the vote's implications for Reagan.

"The votes cast this week will bear directly on the outcome of the arms talks in Geneva and, hence, on the prospects for peace throughout the world," Reagan said in introductory remarks to the Republican senators.

"The president of the United States, the commander-in-chief of our forces, will suffer a majority defeat" if MX production is further blocked, said Armed Services Committee Chairman Barry Goldwater (R-Ariz.) in opening the day's debate. "Uphold the commander-in-chief," he told his colleagues.

While describing the huge weapon and its basing system in existing Minuteman silos as costly and vulnerable as well as an invitation to escalation of the arms race, many opponents stopped short of saying yesterday that a defeat would kill the controversial weapons system.

"This is not a vote on whether to kill the MX. It is a vote on whether to keep our options open," said Sen. Lawton Chiles (D-Fla.), who engineered the cliff-hanging vote that almost sidetracked the program last year and who helped lead this year's fight to block it again.

But Reagan countered that argument with the contention that even a stall in the program would undermine the U.S. bargaining position.

"Some of your colleagues have come up with the idea of simply putting a hold or limit on MX production. I strongly oppose those ideas, as the Soviets will see them for just what they are -- a collapse of American resolve," Reagan said.

Chiles and his allies returned fire by suggesting that the administration was dodging questions about the efficacy of the missile system by "arguing everything but the merits" of the weapon.

"They talk about 'arms control signals.' They talk about 'tests of national will.' They do not talk about what the mission is for the MX or how it fits within the total set of modernization plans for strategic weapons ," Chiles said.

Foes of the missile also challenged the administration's argument that the MX is needed to protect national security and as a bargaining chip at the Geneva talks.

"If we need it, why should it be a bargaining chip . . . . If we don't need it, why spend billions of dollars on it?" asked Sen. Alan Cranston (D-Calif.), the assistant Democratic leader.

"If it's a lousy missile, it's a lousy bargaining chip," Cranston added.

Sen. Edward M. Kennedy (D-Mass.) also challenged the notion that a vote yesterday against the MX could undermine the arms negotiations. "We halted funds for the MX last year, when the two sides were not even talking -- how can the MX be essential now, when the impasse is over and negotiations are actually under way?" he asked.

As for the MX as a demonstration of national will, Kennedy said, "When we put vague expressions about national resolve above common sense in an area as important as nuclear arms control, then we are truly heading toward catastrophe."

Byrd, the Democratic floor leader, also criticized the administration for relying "excessively" on the arms control argument but contended that, on balance, the MX should be approved.

It would help at the bargaining table, add "punch" to the Pentagon's arsenal of strategic weapons and demonstrate U.S. resolve to European allies that have accepted Pershing and cruise missiles on their soil, Byrd said.

Regarding the possible impact on the arms talks, he said, a vote for the MX would be a "manifestation of the political will of Congress" that would mean the Soviets "won't be as likely to sit tight and wait for us to cave in."

Opponents attempted to tie the missile's cost to the budget deficit issue. Contending that the system could wind up costing $40 billion, Cranston said, "The MX, long known as a missile without a mission, now has a mission -- to bust the budget."