The Carter administration won a small but significant first round victory yesterday in its efforts to muster support for a floor amendment that would reshape the tax bill approved last week by the House Ways and Means Committee.

In a meeting with Treasury Secretary W. Michael Blumenthal, liberals on ways and means agreed to unite behind a two-part amendment that would shift the tax cuts toward low-and middle-income taxpayers and trim a cut in capital gains taxes.

At the same time, sources on the House Rules Committee indicated that panel might provide for a separate floor vote on another proposal the administration opposes - an inflation adjustment for capital gains.

The developments were taken as initially encouraging for the administration, which began its effort late Tuesday amid warnings that any new proposals were unlikely to be considered.

House leaders, while sympathetic, appeared cautious about endorsing the administration move. Sources said House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) was "receptive" to the plan, but had "made no commitments."

A Rules Committee source indicated that panel is likely to insist on "evidence of reasonably broad support" before before approving any new floor amendments - evidence the administration still could not provide late yesterday.

The administration proposal is in two parts?

It would shift more of the bill's tax breaks away from upper-income brackets in favor of taxpayers with incomes of $30,000 or less. This would be accomplished by scrapping the committee's plan to raise the personal exemption to $1,000.

Instead, the liberal plan would retain the present $750 personal exemption and raise the $35-per-person general credit now in effect to $100. It also would juggle reductions in tax rate to benefit lower-income taxpayers.

It would trim back the committee's cut in capital gains taxes by subsituting a new plan for the provision now in the bill that would replace the present 15 percent "minimum tax" with a new 10 percent levy.

The administration plan still would repeal the present 15 percent minimum tax. But in return, it would impose a new formula designed to reduce the amount of a capital gain that qualifies for special tax treatment.

The liberals supporting the administration also want a separate vote on a $6 billion proposal by Rep. Richard Gephardt (D-Mo.) to provide a 5 percent tax credit for Social Security payroll taxes. The administration opposes this.

It was still far from certain whether any of these proposals would succeed. ReP. James R. Jones (D-Okla.), who drafted the Ways and Means Committee bill, said his own count showed the liberals would not muster the votes to win.

The liberals measure, which includes the administration plan and the Social Security credit, would be offered as a replacement for two rival substitute amendments that were expected to be offered by Rep. James C. Corman (D-Calif.) and Rep. Joseph L. Fisher (D-Va.).

Both Corman and Fisher were in on the series of meetings yesterday. Neither was available late yesterday, but committee sources said the two had agreed to rally behind the administration's proposals.