Early congressional reaction to President Reagan's new basing plan for the MX missile was skeptical, and leaders of both parties warned yesterday that deployment funds for the MX could well be voted down in the lame-duck session beginning next week unless the administration lobbies forcefully to save them.

Reagan has not lost any major arms votes in Congress since taking office. But on this, "probably, he's going to have one of his greater legislative battles," said Sen. Paul Laxalt (R-Nev.), the senator closest to Reagan.

Sen. John G. Tower (R-Tex.), who as chairman of the Armed Services Committee was critical of the administration earlier this year for failure to propose an MX basing plan, emerged from an afternoon briefing at the White House praising what he called Reagan's "courageous and timely" decision. Tower said he was "cautiously hopeful" that Congress would fund the missile and urged his colleagues not to rush to "ill-informed or hasty judgment."

But the leading Senate opponents of the MX jumped on the new plan before Reagan even announced it. Sen. Ernest F. Hollings (D-S.C.), who failed by only four votes in an effort to delete funding for deployment of the MX in September, predicted that his next effort in the lame-duck session would succeed.

"The Soviets would love us to throw away billions of dollars for a system that could be easily countered," Hollings said at a morning news conference. "We can't afford to throw that many eggs in one basket."

Sen. Carl Levin (D-Mich.), cosponsor of Hollings' amendment to delete funding for deployment of five MX missiles, called Reagan's plan a "nonsolution to a nonproblem," adding: "His decision would make the world more insecure than it is today at the same time that it weakens us . . . . He is violating the SALT II treaty."

The first test for the "Dense Pack" basing proposal is expected to come Nov. 30 when the House Appropriations Committee is to vote on the fiscal 1983 defense appropriations bill. A version of that bill that emerged from the defense subcommittee includes funding for deployment of the MX, but the chairman of the subcommittee, Rep. Joseph P. Addabbo (D-N.Y.), said yesterday he would propose an amendment to delete the funds.

Addabbo called the MX plan, which would cost at least $26.4 billion, "a waste of money" and said it would face "tremendous problems" in the House. A House Republican leadership staff member agreed with the second part of that statement, saying the chances for MX deployment funding "are not all that good . . . ."

Hollings and other MX opponents are also gearing up to delete the MX funds in a continuing resolution the Senate will have to consider if the appropriations bills are not passed during the lame duck. Yesterday Hollings disclosed a "Dear Colleague" letter opposing the missile that was signed by eight colleagues, including Republicans Mark O. Hatfield (Ore.) Nancy Landon Kassebaum (Kan.) and David F. Durenberger (Minn.).

Three Wyoming politicians -- Democratic Gov. Ed Herschler and Republicans Sen. Malcolm Wallop and Rep. Dick Cheney -- said they supported Reagan's decision to base the MX in their state.

Herschler noted that there are already Minuteman missiles in the area and that the MX project might provide as many as 6,000 jobs at one time.

Opponents, however, contended that the Air Force had failed to consult the people of Wyoming as required by law. "Ranchers and many townspeople oppose having the MX on prime Wyoming ranchland," said Sister Frances Russell of the Tri-State Coalition, an anti-MX group based in Cheyenne.

Several congressmen and committee staff members yesterday said the votes on the MX may depend on the intensity of administration lobbying.

"You've got to remember that Reagan has never lost a big-ticket defense item," said one Democratic Senate staff member. "If he calls in a lot of chips over the next few weeks, he could pull it off. One question a lot of us are thinking about is whether the president would mind that much if the MX is defeated by the Democrats. He's never seemed all that hot for it in the past, and if the Democrats kill it he could say they're soft on defense."