President Reagan yesterday gave a month's extension to the Commission on Strategic Forces in its effort to find a politically acceptable strategic weapons plan that will include the basing of MX intercontinental ballistic missiles in existing Minuteman silos.

Administration and congressional sources said that the weapons proposal, which in its present form also includes plans for a small future mobile missile, is being shaped in consulation with key congressional Democrats.

These Democrats recommended that the strategic package be delayed so as not to be the first defense issue to come up in a new Congress grown increasingly restive over military spending.

One House member involved in the negotiations, Rep. Les Aspin (D-Wis.), reportedly told Brent Scowcroft, head of the 11-member commission, that "if it's the first vote on defense it goes right to the ground."

Democrats in the House also have urged that the package be put together "in an arms control context," according to one source, and because of the proposed small new missile this could require a revision of the president's strategic arms reduction (START) proposal now under discussion with the Soviets at Geneva.

"MX and arms control are headed for a shotgun wedding," said one key Democratic congressional aide.

An administration official said that "any and all" compromises are possible as long as they meet the president's requirement for prompt deployment of the MX, which can be achieved readily only through use of existing silos. Scowcroft yesterday alluded to the necessity for a consensus solution after giving the president a 15-minute progress report on the commission's deliberations.

"Look, the program has been in difficulty, is in difficulty," Scowcroft told reporters outside the White House. "What we are trying to do is arrive at a solution which will achieve the kind of acceptability of the leadership of the government in both houses that will enable our strategic programs to go through."

Reagan spent only 15 minutes of a two-hour meeting with the commission. He was "just listening," said one official, and did not ask questions about the various options under consideration.

Scowcroft said that the panel, which had been scheduled to make recommendations by Feb. 18, would now report to the president near the end of March, but added that no date had been set.

"I'm hopeful the commission will reach a consensus," Scowcroft said. "I'm not at the point of saying whether that will be possible."

The possibility rests chiefly on the administration's ability to find some way of winning the support of middle-road Democrats, especially in the House, without alienating defense conservatives of both parties, particularly on the Senate Armed Services Committee, which in 1981 opposed the administration's first plan to put the MX into existing silos.

To accomplish the latter purpose the administration has been wooing the ranking Democrat on Armed Services, Sen. Henry M. Jackson (D-Wash.), who recently was a dinner guest of Reagan at the White House.

The administration also expects to win over Senate Armed Services Chairman John G. Tower (R-Tex.). Tower led opposition to the 1981 proposal on grounds that existing silos would leave the MX vulnerable to attack.

The problem throughout has been to find some way to reduce the missile's vulnerability without adding greatly to its cost or incurring other objections.

The precedent for the commission approach was the recently achieved bipartisan Social Security compromise in a similar situation where the conflicting views at first seemed unreconcilable. In that instance, another presidentially appointed commission reached a consensus in which both sides yielded fundamental ground.

What the president would get out of the compromise is immediate approval of production funds for the MX missile, which was rejected by the House Dec. 7. The administration's most persistent argument with Democrats is that the United States cannot appear to be backing away from a new land-based missile at the same time its European allies are being asked to accept new missiles on their soil.

In order to win the middle-road Democrats, administration officials have discussed dropping the "Dense Pack" basing system under which 100 MX missiles would be grouped in a one-mile-wide, 14-mile-long series of 100 superhardened silos in Wyoming.

In order to win the conservatives, placement of the missiles in existing silos is being presented as an interim solution in which the MX would be augmented by another generation of small, single-warhead ICBMs to be made survivable against a Soviet attack through mobile transport or deep underground basing.

The small ICBM has the added attraction of being a course proposed by many of the same middle-roaders that are the prime targets of the new White House bipartisan approach. Discussions have begun on how the president's START proposal could be revised to allow for more missile launchers than he has presently proposed.