President Reagan's Commission on Strategic Forces, which is having difficulty finding an MX missile basing system that would be technically feasible and politically acceptable, will seek an extension of its Feb. 18 deadline for making a recommendation to the White House, administration sources said yesterday.

"We're not going to report until we're done," said a high-ranking official, who acknowledged difficulties in devising a proposal that would win consensus backing within the administration and broad enough political support to gain approval by Congress.

At this point, according to commission sources, the 11-member panel appointed by Reagan is leaning toward a two-phase solution that might not satisfy these criteria.

In the first phase, up to 50 of the controversial new MX intercontinental nuclear missiles would be put in existing Minuteman missile silos in Wyoming.

This would satisfy the White House requirement that initial deployment take place by 1986, but a similar Reagan administration plan was rejected by the Senate.

The second phase, intended to meet U.S. missile needs of the 1990s, includes a variety of long-term proposals. Some members of the commission favor continued studies of deep underground basing for the MX and new studies on a small, single-warhead ICBM that could be placed in a silo or made mobile.

The mobile options include moving the missile around by truck or in an armored carrier or from one launching spot to another by helicopter.

The commission, appointed by Reagan Jan. 3 to find an MX solution after the House rejected $988 million in production funds for the missile during last year's lame-duck session of Congress, will meet with Reagan for the first time today to discuss the options.

One problem with the direction in which the commission is heading, administration officials said, is that any proposal for deploying MX missiles in existing Minuteman silos is certain to be opposed in Congress on grounds that it would leave the missiles vulnerable to Soviet attack. To head this off, the commission wants to continue research and development of superhardening the existing silos, eventually building more and rotating the MX missiles among a larger number of silos, according to commission sources.

At present, the sources said, a majority of the commission opposes endorsement of the administration's most recent Dense Pack basing plan, in which 100 MX missiles would be deployed in 100 closely spaced superhardened silos.

Integral to the commission's currently favored plan is continued development of the Trident II missile, a submarine-launched missile planned to match the capability of the MX to destroy Soviet missile silos.

Administration officials said that the commission, working closely with the White House and key members of Congress, is trying to come up with a total plan that will satisfy the many critics of the MX.

The White House has recalled Max Friedersdorf, the lobbyist who pushed the admininstration's economic package through Congress in 1981 and was rewarded with an ambassadorship, from Bermuda to sound out Congress on what would be an acceptable plan. The search for a new MX basing system has been going on since Reagan, during the presidential campaign of 1980, opposed President Carter's proposal to build 200 MX missiles and rotate them among 4,600 shelters in the Nevada and Utah deserts.

After the election, Reagan's secretary of defense, Caspar W. Weinberger, appointed a 15-member commission of experts to study a new proposal.

What Reagan and Weinberger came up with on Oct. 2, 1981, based on a variant of what the commission recommended, was putting the first MX missiles in existing silos while research continued on a long-term solution. This was promptly rejected by the Senate, which told the White House that Congress wouldn't put the missile anywhere until a permanent basing system had been approved. Nearly a year later the administration came up with Dense Pack, which would have concentrated the missiles in a strip one mile wide and 14 miles long on a Wyoming air base.

On Dec. 7, 1982, the House in effect rejected Dense Pack and turned down production funds for the MX by a 248-to-176 vote. Subsequently, it was disclosed that three of the five members of the Joint Chiefs of Staff also opposed the Dense Pack plan.

Sources said that Friedersdorf, who is working out of the office of presidential assistant Thomas C. Reed, the vice chairman of the commission, reportedly has been concentrating on winning the support of middle-road House members who opposed the administration in the December vote.

But there is concern among MX supporters that this will provoke the opposition of conservatives on defense issues in both houses who helped derail the previous proposal to put the MX in existing silos, in addition to congressional liberals who oppose the MX in any form.

The smaller missile option has attracted increased attention in the administration and gained popularity on Capitol Hill. But its opponents point out that it couldn't be ready before 1990 and that from 3,000 to 5,000 of these missiles would be needed to counteract the threat from much larger Soviet missiles with multiple warheads.

Deployment of this magnitude would violate the SALT I nuclear arms limitation treaty, the unratified SALT II treaty limits by which the United States has voluntarily abided, and Reagan's proposal for strategic nuclear arms reduction.