Rebounding from a serious domestic policy defeat only a day before, President Carter turned on the heat today and won a strong Democratic National Convention endorsement of the administration's planned MX mobile missile system.

By a vote of 1,874 to 1,277, the convention rejected a minority plank opposing the controversial new strategic weapon as introducing "new risks which outweigh apparent military advantage."

Stung by convention rebuffs Tuesday to administration positions on economic and women's issues, Carter forces -- led by Defense Secretary Harold Brown -- mounted a full-court press to win on the MX issue.

As signs reading "MX -- Disaster on Wheels" and "Ban the X-Rated Missile" sprouted on the convention floor, wavering Carter delegates were summoned to Carter trailers outside the hall for heavy persuasion from brown and others.

But the biggest gun was a personal, hand-scrawled letter on White House stationery from Carter to all convention delegates that read:

"As commander-in-chief of American armed forces, my responsibility to protect this nation is paramount. It is crucial that our strategic nuclear forces not be vulnerable to a preemptive Soviet attack. The MX missile system is our optimum means of meeting these vital goals.

"We Democrats must demonstrate to our nation and to the world that we are committed to defending our country, and to concluding a balanced nuclear arms control agreement. Therefore, it is very important for you to vote NO on Minority Reports 20 & 23 [the two dealing with MX system]."

A letter was circulated on the convention floor citing support for the MX system by the high command of the AFL-CIO, which only the day before helped lead the successful fight to endorse, over strong administration objections, a $12 billion antirecession jobs program. However, an AFL-CIO spokesman said the federation was not lobbying its members on the issue. But the ardently pro-Carter National Education Association campaigned for Carter on the issue.

The frenzy of lobbying -- as intense as any the Carter forces have mounted since Carter nailed down the nomination Monday night in the rules fight over binding delegates to their earlier commitment -- came amid early afternoon reports that the White House was in danger of losing.

But presidential press secretary Jody Powell rejected suggestions of the type of compromise that Carter forces tried unsuccessfully to work out on the economic planks the day before. "There is no possible way that the president of the United States can negotiate away a vital strategic weapons system" in a political deal at a party convention, he said.

Carter's abrupt capitulation on most of the economic issues the previous evening embittered some of his convention floor whips, making it all the more difficult to hold the line on the MX vote -- as critical to defense policy as the antirecession plank was to domestic policy. "I've had it with these people," said one Carter floor operative, speaking of the president's top political team. "They are really bush league."

In a late afternoon debate that drew only casual attention from delegates, Defense Secretary Brown defended the multibillion-dollar MX -- a new land-based mobile missile intended to replace the Minuteman system -- as essential to deter a nuclear attack on the United States.

Retired Lt. Gen. George Seignious, former administration disarmament chief, similarly characterized it as a keystone for continued disarmament efforts because the country can "never negotiate from fear" of nuclear vulnerability.

The author of the anti-MX plank, Oregon Democratic Chairman Joe Smith, took pains to stress that the MX dispute, was not a fight between Carter and his withdrawn challenger, Sen. Edward M. Kennedy of Massachusetts, although most Kennedy delegates appeared to line up behind him on the anti-MX side. "I am a loyal Carter delegate," Smith told the convention, "and I am here because I see the country I love about to make a tremendous mistake."

In the midst of the MX debate, the Kennedy forces reached a compromise in a dispute over draft registration -- tilted in Kennedy's favor in that it called for registration only in the event of an emergency.