The Reagan administration, which only two months ago won an impressively easy victory in the House in its vote-by-vote struggle for continuing congressional approval of building the MX missile, yesterday saw that bipartisan coalition begin to erode in the face of renewed skepticism about the White House's commitment to arms control.

Reacting to an intense lobbying campaign by nuclear freeze advocates around the country and what they saw as lack of progress in arms control negotiations with the Soviet Union, 18 House Democrats, led by Majority Leader James C. Wright Jr. (D-Tex.), broke away from the administration's coalition.

After winning 91 Democratic votes in May for approval of a basing mode and the start of flight testing for the nuclear multiple-warhead MX, the administration was able to hold on to 73 Democratic votes last night to pay $2.5 billion for procurement of the intercontinental ballistic missile.

In the end, after a tense day of lobbying and vote-counting that continued up to the final minutes, President Reagan's 13-vote victory was somewhat more comfortable than had been expected.

But what happened yesterday in the House, according to opponents of the MX, was a clear signal that the fight over the controversial missile is far from over and that, as the 1984 presidential campaign heats up, congressional Democrats are likely to push the administration even harder to show progress on an arms treaty before the next crucial MX vote.

"I think the message is that the House is trying to maintain control on the issue--and that they're very, very edgy," one Democratic aide said. "They don't want Reagan to feel they've signed off on his approach to dealing with the Russians."

The good will the president had gained through the Scowcroft commission's recommendations on arms control has ebbed quickly, and it will be harder in the future for him to use its arguments to sell the MX to nervous Democrats, according to a number of those who voted with Reagan in May but against him yesterday.

Earlier this week, it became apparent the White House was running into trouble on the MX, and administration officials began a rear-guard action to limit the defections among Democrats who had supported them last May.

The calls came from Reagan, Vice President Bush, Secretary of State George P. Shultz, Defense Secretary Caspar W. Weinberger, Arms Control and Disarmament Agency chief Kenneth L. Adelman and even from U.S. arms control negotiators, all with a simple message: the president is committed to arms control, so don't desert us now.

But equally as intense was the lobbying from such groups as Common Cause and from arms control advocates who have become increasingly well-organized at the grass-roots level. House Democrats who earlier had supported Reagan acknowledged they have been impressed by the strength of support in their districts for a nuclear freeze.

The most important Democrat to part company with Reagan on the MX yesterday was Wright, who in May had voted, to the dismay of many junior Democrats, to support basing studies and flight tests.

"I have been inexorably forced to face the fact that there is no such thing as compromise unless the president writes out the compromise and hands it to you," Wright told reporters. "As far as the president is concerned, bipartisanship is a one-way street."

Rep. Richard A. Gephardt (D-Mo.) also defected, despite a call yesterday morning from the vice president. Saying that he still supported the goals of the Scowcroft commission, Gephardt said he decided to vote against MX procurement money this time because "I had a concern about their basic view on arms control."

Saying he questioned "who is in control of arms control policy , who's driving it and just what their view is," Gephardt added that the administration wanted Congress to vote for the MX in return for promises on arms control that might not be fulfilled.

"There is not much trickle-down on arms control," said Rep. Dan Glickman (D-Kan.), another Democrat who turned against the administration yesterday despite calls from administration officials. "I think the president's intentions are good, but I don't feel that has trickled down to his advisers."

Other Democrats said that statements by administration officials since the last major MX vote in May suggested it was missing negotiating opportunities with the Soviets.

Rep. Martin Frost (D-Tex.) cited this as a reason that he was wavering before he responded to a personal telephoned plea from Reagan and voted for the MX one more time last night. He said he came away from a recent visit to the Soviet Union, as part of a congressional delegation, convinced that the Soviets are prepared to negotiate seriously.

"The Soviets sent all kinds of signals," Frost said. "I'm concerned that the president and some of his people are not responding as quickly as they could."

In the case of Wright and several other influential Democrats, personal political aspirations may have played a role in opposition to the MX.

"It's clear the majority of the Democratic Party in the House is fairly liberal on these issues, and I think the leadership is being responsive," said one Democrat who asked not to be identified.

Of more immediate importance is the role that arms control issues are likely to play in the presidential campaign. Democrats still appear somewhat divided on the best political strategy to follow.

One approach is to give Reagan what he wants and, if he fails to produce an arms agreement, attack him during the campaign. Another approach, which seemed to gain favor in recent weeks, is to refuse to give Reagan the MX and keep the pressure on for serious negotiations.