The Carter administration gave its support yesterday to a liberal-backed plan for averting a sharp cut in capital gain taxes, but the proposal seemed unlikely to prevail as the House Ways and Means Committee resumed its work on the president's tax-cut bill.

Without formally endorsing the liberal's plan, Donald C. Lubick, assistant secretary of the treasury for tax policy, termed the proposal "the best we've seen so far" among a spate of rival Democratic and Republican measures dealing with capital gain taxes.

However, panel sources continued to predict that prospects for the liberals' plan are dim. Instead, the Ways and Means Committee is expected to approve a capital gains tax-cut plan by Rep. James R. Jones (D-Okla.) that Carter so opposes he said he would veto.

Meanwhile, panel members raised the possibility yesterday that the Jones bill may be turned into a "Christmas-tree" package, laden with special-interest amendments tacked on at the last minute. Among the prospects: A $3 billion tax break for charities.

The committee's session yesterday marked its first meeting since April, when panel leaders abruptly called a recess following a round of defeats for Carter's "tax reform" proposals. Much of its time since has involved behind-the-scenes bargaining over capital gains.

The plan supported by the administration, drafted by Rep. Joseph L. Fisher (D-Va.), would hold the cut in capital gain taxes to $688 million, compared to revenue losses of $1.3 billion and $2.2 billion in competing bills by Rep. James R. JOnes (R-Okla.) and William A. Steiger (R-Wis).

Unlike the Jones and Steiger provisions, however, the Fisher bill would not roll back the "minimum tax" imposed on capital gains in 1969 - a move that Carter especially opposes.Instead, it would merely exempt residential home sales by the elderly and allow a break for venture capital.

Capital gains are the profits from the sale of stocks or other assests. Under present law, only half a capital gain is subjected to taxes. The minimum rate for capital gains now is 49.1 percent, although the top rate is paid only by a handful of high-income taxpayers.

Steiger's plan would reduce this to 25 per cent, while Jones' bill would trim it to 35 per cent - in both cases by eliminating the imposition of the "minimum tax" on the portion of capital gains not subject to the income tax. Carter has called both measures "millionaire's bills."