The Carter administration's new last-ditch effort to win support for a $15 billion stripped down version of its tax cut ran into serious trouble yesterday in the House Ways and Means Committee - dampening already-slim prospects that the tactic could succeed.

Without taking any formal votes on the package, Democrats on the panel generally reacted negatively to the new White House plan, ending a conference with Treasury Secretary W. Michael Blumenthal with little more than grudging agreement to give the President more time.

However, Rep. Al Ullman (D-Ore.), the committee's chairman, expressed serious doubts that the administration would be able to muster much support for its proposal, which was intended as a tactical move to head off a possible cut in capital gains taxes.

Ullman said he intended to give the administration "until mid-July" to try to win members over to its new proposal, and then would "go back to" a compromise by Rep. James R. Jones (D-Okla.) that includes both a capital gains tax cut and a graduated income tax for corporations.

The Ways and Means chairman said that while he would provide the "19th vote" needed to report the administrations's plan out of committee, he did not intend to take the bill to the floor if it appeared likely to turn into "a donnybrook."

He particularly expressed reservations about the administration's hopes of opening the bill up to floor amendments in order to try to restore some of Carter's "tax reform" proposals. If floor amendments ultimately are permitted, he said, the capital gains tax cut "willpass."

The committee's reaction appeared to mark a further setback for the administration, which has seen the bill shrivel from the $25 billion, reform-laden proposal that Carter unveiled in January to a $15 billion, largely middle-income tax cut devoid of any so-called "reform."

Blumenthal conceded yesterday his presentation of the plan to the Democrats had produced "a lot of discussion" and "a great variety of views." Congressional sources indicated there was virtually no support within the panel for the administration plan.

The $15 billion no-frills proposal already has been rejected informally by the panel. Ullman first tried it out on members several weeks ago in exploring avenues for a possible compromise, and Rep. Joseph L. Fisher (D-Va.) renewed the plan on Wednesday, with little apparent success.

Ullman said yesterday he was certain he could muster "a clear majority of the committee" and "a majority of Democrats" as well for the Jones compromise, which panel leaders effectively agreed to late last week but then shelved after protests from the administration.

The administration objects to two elements in the Jones proposal - a measure to cut taxes on capital gains, and a plan for a graduated income tax for corporations. The capital gains measure is a watered-down version of a bill sponsored by Rep. William A. Steiger (R-Wis.).

Ullman predicted yesterday that if the tax bill were opened to floor amendments, not only would the steiger bill pass, but the House also might tack on a GOP across-the-board tax-cut proposal, the graduated corporate income tax and several other conservative measures.