Washington — The future of the MX missile, which has weathered a decade of controversy, now appears to rest with the outcome of this fall's congressional elections. Congressional leaders, with apparent compliance from the White House, are now working out a plan to delay a decision on the 10-warhead nuclear weapon until next year. By then the new Congress will be sworn in, either with more pro-defense Reagan Republicans or with enough skeptics to kill the MX.
''It's moved over to the public arena,'' says Rep. Les Aspin (D) of Wisconsin. He has forged a coalition to save the weapon, which has been surviving by only a handful of votes this year.
The debate over the missile has been one of the snags holding up defense legislation, the budget, and a collection of spending bills that Congress must pass before it adjourns Oct. 5. An agreement to delay the MX question appears to satisfy all parties, including the missile's foes, who have been encouraged by the growing opposition to the MX on Capitol Hill during the past year.
Opponents are now ''going for the knockout punch,'' says Rep. Les AuCoin (D) of Oregon, a leader in the anti-MX effort, who points to the shrinking support for the MX in recent votes.
''Now the advocates are hanging desperately to the hope'' that the MX will be authorized but the money withheld until Congress votes next spring on whether to spend it, says Representative AuCoin. ''That's a tremendous change in the political landscape.'' It has long been an axiom in Congress that weapons systems never die, but the MX has come close during the past year, even in the GOP-controlled Senate. The upper chamber last June defeated a proposal to kill the MX only after Vice-President George Bush cast the tie-breaking vote.
Opponents charge that the missile's stationary launch sites would be vulnerable to attack, that the weapon would be seen as a first-strike weapon, and that it is a waste of defense dollars. The House has already voted to cut off funds for new MX missiles unless Congress passes a resolution next year authorizing that the money be spent. Moreover, both houses have cut back on President Reagan's request for missiles, which would be put in 100 existing Minuteman missile silos.
The mood on Capitol Hill ''reflects more closely the attitude on the part of the public that enough is enough,'' says AuCoin of the MX, which is estimated to cost between $21 billion and $30 billion. He says that members of Congress have been moved by public concerns about arms control and about the federal deficit.
Even if Mr. Reagan wins by a landslide that brings more Republicans into Congress, AuCoin maintains that ''we'll have a larger number of votes'' in both houses to oppose the MX.
However, Representative Aspin is not convinced of the trend. ''Let's see who gets elected,'' he says, adding that the new Congress might be friendlier toward the weapon. ''We will know on election day or the day afterward,'' he says.
He holds that his support for the missile has not wavered - a stance aimed at shoring up a public view of his party as being too soft on defense.
''The public sees Reagan as plenty tough'' but unwilling to negotiate, he says, while his own party members are ''willing to negotiate'' but not to build weapons. ''You've got to have something to negotiate,'' he said, citing Soviet land-based missiles, comparable to the MX, as the weapons that have most concerned the US.
While the fight over the MX has been the most prominent sticking point in the defense bills, Congress has other major defense problems. At this writing, lawmakers and the White House were still bickering over a total 1985 defense budget. The House has approved $285.7 billion; the Senate has voted $299 billion. Congress also is debating whether to permit the launching of antisatellite weapons against test targets in space. And a major decision on Reagan's so-called ''Star Wars'' ballistic missile defense program would be left to the next Congress.