President Reagan has thrown congressional opponents of the MX missile on the defensive by timing a crucial vote on the missile for the week after arms control talks with the Soviet Union resume in Geneva. Lawmakers said the move appears to have brightened prospects for approval of the nuclear weapon.

In the Democratic-controlled House, MX supporters said they believe they could have a 10- to 30-vote margin in favor of the multiple-warhead missile, depending on how well the arms talks, set for March 12, appear to be going. House MX opponents acknowledge that a vote will be close but have not ruled out winning it.

In the Republican-led Senate, MX critics say that a slim majority of senators -- possibly 51 or 52 of the 100 -- might oppose further funding for the MX, in part because its high cost would be hard to justify in a time of budget cutbacks. But one Senate official said, "Quite frankly, the atmospherics of the arms control talks surrounding the vote favor the president."

In addition, lawmakers said, Congress rarely has voted to deny a president any program given such high priority. Last fall, Congress voted to freeze funding for 21 of the MX missiles that Reagan requested, leading many to predict Congress would make him the first president to be denied a major strategic weapons system.

On Tuesday, Reagan began a new drive to win congressional approval of the construction of the 21 missiles, saying he was "utterly convinced" he could not get a "sound agreement" from the Soviets without it.

Under a complicated arrangement, Congress approved the $1.5 billion necessary to fund the missiles but froze the funding at least until March 1, when Reagan could renew his request for it.

Each chamber of Congress would then cast two votes: one to authorize production of the 21 missiles and another to unfreeze the funding.

Administration officials have indicated that they will submit the necessary request to release the funds, possibly by Monday, which would lead to a vote in both chambers beginning around March 20.

"It's going to be tough fight, no doubt about it," said Rep. Nicholas B. Mavroules (D-Mass.), a leading MX opponent, adding that the Reagan administration argument that the MX is needed for the arms control talks "is a heavy club," particularly for Democrats worried that the country views Democrats as too "soft" on defense issues.

That is apparently one of the reasons House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) has insisted that the Republican-run Senate vote first on the MX.

O'Neill has told some House Democrats privately that "it would be better for the country" -- and presumably the Democrats -- if the Senate killed the MX, a Democratic source said yesterday.

In the Senate, MX opponents are looking into several possibilities for making a vote against the MX more palatable, including accompanying it with a "sense of the Senate" resolution stating that the Senate in no way was interested in killing the MX, only slowing it down, sources said.

Meanwhile yesterday, former defense secretary Harold Brown and retired general Brent Scowcroft told a special defense policy panel of the House Armed Services Committee that Congress should continue to fund the MX as a "bargaining chip" for arms control negotiations.

When asked by Rep. William L. Dickinson (R-Ala.) whether a vote against the MX would cause "irreparable harm, if not wreck" the Geneva arms talks, Scowcroft, who headed the commission that recommended the MX program now in place, said it would "show the Soviet Union that there are substantial advantages to talking but not doing anything in Geneva."