With 10 nuclear warheads, each carrying the explosive power of 300,000 tons of TNT, the MX intercontinental ballistic missile might not seem to fit Wisconsin Democratic Rep. Les Aspin's description as "the homeless waif of weapons."

But the MX, after more than a decade of debate and $8 billion, remains the most hotly contested element of the administration's nuclear weapons buildup. In a few months, the MX -- dubbed Peacekeeper by President Reagan -- might become the first major nuclear system ever denied a president.

Congress is scheduled to vote in late March or early April on whether to continue production of the MX, a decision that an uncertain and almost evenly divided Congress postponed earlier this year.

The outcome of that vote could hang on such disparate factors as Soviet Foreign Minister Andrei A. Gromyko's mood when he emerges from arms control talks with U.S. officials in January, and on senator-elect Albert Gore Jr.

The Tennessee Democrat, who voted to continue MX funding in the House this year, has become a Senate swing vote. He refused to say how he will vote, but indicated that he remains flexible.

The vote is likely to be one of the first major tests of Reagan's sway over the new Congress in his second term. It also could be pivotal to the missile's future, because the Air Force says that the program will pass the halfway point in funding if Congress agrees to spend about $1.5 billion for 21 missiles in fiscal 1985.

The battle over those funds will be complicated by a concurrent fight over the fiscal 1986 budget, in which the Defense Department plans to seek $3.7 billion for 48 MX missiles and associated research and construction costs, according to Air Force officials. With the impact of 43 new House members still unclear, few observers are willing to make predictions.

"I think the prospects are good that we can stop the funding," Rep. Les AuCoin (D-Ore.), a leading MX opponent, said last week.

But Air Force Brig. Gen. Gordon E. Fornell, who heads the MX program, said, "I feel we have a very good chance to win this special vote . . . and proceed with the program in a logical way."

Fornell, a former test pilot, said the MX is within budget and on schedule for an initial deployment of 10 missiles in December 1986. He said that after six test flights, with a seventh scheduled for next month, the MX development is on its way to becoming "one of the most highly successful flight test programs ever."

But Fornell said he also realizes that the MX program has become politicized and will not be judged by the "normal" criteria of cost, schedule and performance.

The MX, for "missile experimental," originally was said to be necessary because Minuteman III missiles, stored in concrete "silos" in the West, had become vulnerable to increasingly accurate Soviet missiles. But the Pentagon never developed a politically acceptable plan to base MX in a less vulnerable way.

The Carter and Reagan administrations considered basing 34 options, rejecting each because of cost, local opposition or technical problems. "We considered dropping it out of planes, burying it thousands of feet underground, shuttling it around racetracks, even hiding it inside disguised beer trucks," Aspin said.

Finally, the Reagan administration decided to put the MX in the same Minuteman silos, pledging at the same time to develop a mobile, smaller missile that would be ready in the early 1990s. Although no less vulnerable than the Minuteman, officials said, the MX is needed because it will be more accurate than earlier intercontinental missiles.

Fornell said accuracy is needed to threaten Soviet missile silos and command bunkers that have been "hardened" to withstand all but direct nuclear hits.

Critics counter that such accuracy makes sense only if the United States wants to attack first and destroy Soviet missiles before they are launched from their hardened silos.

Many members of Congress have said they have trouble supporting the official justifications for the MX but believe that it must be built because the Soviet Union is building similar weapons.

Aspin, who helped build the coalition of hawks and liberal House Democrats that has allowed the MX to survive so far, relied on that argument in a speech, saying, "In the last analysis, it was thought the MX would provide a good bargaining chip. We could give up the MX in exchange for a reduction in the number of Soviet warheads . . . . If we unilaterally cancel our weapon systems, like the MX, they are not likely to reduce their equivalent systems."

The "bargaining-chip" defense means that talks between Gromyko and Secretary of State George P. Shultz, set for January in Geneva, are likely to play a major role in how Congress handles the MX this spring. But there is no agreement on whether successful talks will help or hurt the missile.

Rep. Joseph M. McDade (R-Pa.), who will become the ranking minority member of the House Appropriations defense subcommittee next year, said the talks will produce a "dramatic change of atmosphere" that will help the MX. "You don't give it away before you sit at the table," he said.

But McDade also said that the talks "cut both ways." Few members will want to vote billions of dollars for a weapon that they believe is about to be negotiated away, he said.

During Reagan's first term, the MX survived by increasingly narrower margins in the House, winning last May by 218 to 212. In the Senate, an effort to block 1985 production failed 49 to 48, with Vice President Bush breaking a tie.

Last month's elections probably helped the MX slightly in the House, where Republicans picked up 14 seats, and hurt in the Senate, where the Democrats gained two. But so many freshmen and veterans are keeping their options open that no one can count votes with assurance, according to MX opponent Rep. Joseph P. Addabbo (D-N.Y.), chairman of the Appropriations defense subcommittee.

Gore, who joined Aspin in supporting the MX last year to the dismay of many Democrats, is a prime example. Gore declined to discuss his position last week, but in response to a request he issued a short statement that appears to leave room for flexibility.

"Arms control will continue to be my top priority in the U.S. Senate," the statement said. "So long as the administration demonstrates it is serious about negotiating with the Soviets, I am willing to continue in a bipartisan effort to reach an agreement."

MX opponents hope they can persuade Democratic senators who reluctantly supported the missile in the past, such as Sen. Sam Nunn (D-Ga.) and minority leader Sen. Robert C. Byrd (D-W.Va.), to change. Even without such help, Michael Mawby, political director of the anti-MX organization SANE, said that he believes the election left the Senate with 51 MX opponents.

In the House, Mawby said SANE polling shows that the 43 new members, 31 of whom are Republican, include eight new MX opponents, six new supporters, 16 seats in which there has been no change and 13 who are undecided or whose positions are unknown. McDade said that he believes that the House will vote for the 21 MX missiles for 1985 and will seek some compromise for 1986, but he said the votes will be close.

"I don't know anybody who campaigned on building the MX," he said.

Still, several leading MX opponents, including Addabbo and Rep. Nicholas Mavroules (D-Mass.), said that they do not have the votes to kill the missile outright. But they said they may be able to continue holding up production funds.

"Things can change between now and April," Mavroules added. "I think it's going to be one hell of a battle.