President Reagan sought yesterday to convert bipartisan backing for next week's U.S.-Soviet arms control talks into overwhelming congressional approval for the MX missile, and was making inroads among Democratic House members on both issues.

Democratic congressional leaders met with Reagan at the White House to discuss the talks that will resume in Geneva on March 12. "We wish them well, we want them to succeed and whatever we can do to assist that we should do," said House Majority Leader James C. Wright Jr. (D-Tex.). "Partisanship must stop at the water's edge," he said.

Senate Minority Whip Alan Cranston (D-Calif.), a foe of the MX, said to Reagan's chief arms control negotiators in a meeting in the Cabinet Room: "If you bring back a good treaty, and I presume you will bring back a good one or none at all . . . I will do all I can to see that those on the Democratic side of the aisle move to swiftly ratify it."

Meanwhile, sources in congress said that House Armed Services Committee Chairman Les Aspin (D-Wis.), one of the most influential members of his party on defense issues, had told House Democratic leaders that he would support the MX. Aspin had been considered a questionable vote on the issue.

White House spokesman Larry Speakes said the administration expects a "very close" vote on the nuclear missile in both houses. But other officials, without providing names, said that the administration had made strong gains among undecided members of Congress because of the president's efforts this week.

Speakes said that Reagan had talked to Wright by telephone and that the majority leader had agreed to send a House delegation to observe in Geneva. On Monday, Wright canceled the House trip after reading what he described as derogatory statements about the delegation in the Rowland Evans and Robert Novak column.

The White House spokesman denied that administration officials had said that congressional observers were threatening to turn the arms talks into a "circus."

The White House yesterday continued to mount an all-out political effort to free $1.5 billion frozen by Congress last year for the production of 21 additional MX missiles, which Reagan calls the "Peacekeeper." The 10-warhead missiles are part of a force of 100 that the administration ultimately intends to place in existing Minuteman missile silos.

Reagan has talked to more than 100 members of Congress this week on behalf of the MX. In a speech to business leaders at the White House yesterday he maintained that approval of the 21 missiles, in a vote timed for about a week after Geneva negotiations resume, was essential to success of the arms control talks.

"The vote on the Peacekeeper is also a vote on Geneva . . , " Reagan said. "Rejecting the Peacekeeper will knock the legs out from under the negotiating table, leaving the Soviets no conclusion but that America lacks unity and resolve. I can think of no greater disaster for the negotiating position of the United States. Weakness does not make for good negotiations."

Arguing that "the credibility of deterrence will vanish" if Congress fails to approve the MX, Reagan invoked the words of presidents Calvin Coolidge and Theodore Roosevelt and the late Sen. Henry M. Jackson (D-Wash.) on behalf of a strong defense.

He also quoted from a letter sent by Soviet dissident and Nobel laureate physicist Andrei Sakharov, whom Reagan said had written a friend in the West "that arms control talks would be easier if the U.S. were to have the MX."

"Peace is not easy to maintain," Reagan said. "It will take hard work and diligence. It will take unity and sense of purpose, and, yes, it will cost money. This generation of Americans must meet the test."

Reagan's speeches and meetings yesterday capped an intensive three days of lobbying in which the White House has put out repeated statements in an effort to dominate the dialogue on arms control, the MX and the president's controversial Strategic Defense Initiative (SDI), often called "Star Wars."

The administration gained support on the latter issue from visiting Italian Prime Minister Bettino Craxi, who told a joint session of Congress that his country supports research into strategic defense.

In his speech Craxi said it is "still necessary that our deterrent capacity be strong and that it be updated as the progress of science and technology continues."

But at a news conference on the third and last day of talks between members of Congress and 30 visiting Soviet officials, the head of the Russian delegation reiterated his opposition to "Star Wars."

"If it happens, we'll be forced to take adequate measures -- and first of all through strengthening our strategic systems," said Vladimir V. Shcherbitsky, a member of the Supreme Soviet and the Politburo.

Rep. Thomas S. Foley (D-Wash.), who hosted the Soviet visitors, said the discussions were "frank" and that some of them also were "difficult."

On the MX issue, the administration was particularly pleased by the backing of Aspin, who had announced that he might abandon his support of the missile this time in favor of supporting the Strategic Defense Initiative.

But sources said that at a meeting Monday with Wright, Foley and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), Aspin said that the 21 additional MX missiles should be available to be negotiated away in arms talks.

"He said it made sense to use it as a bargaining chip," said one source familiar with the meeting.

Aspin was instrumental in the past in helping the administration win House approval of the MX. However, MX critics were convinced he would change his position this year because of the crucial role liberal Democrats played in helping him get elected last January as Armed Services Committee chairman.

On the issue of the arms control negotiations, the administration received accolades from leaders of both parties yesterday and many of them approvingly quoted Wright's statement about partisanship stopping at the water's edge.