A key economic adviser to the Reagan administration, Alan Greenspan, said yesterday he favors delaying a cut in personal income taxes until midsummer.

Greenspan, a former chairman of the Council of Economic Advisers who heads his own consulting firm, said he would like to see taxes cut "as soon as feasible" but not made retroactive because of problems associated with changing tax liabilities once a tax year has begun.

However, delaying the beginning of the three-year, 30 percent cut in personal income tax rates promised by President Reagan could decrease the drain on fiscal 1982 federal revenues by more than $35 billion.

In "get-acquainted" sessions yesterday with House Democratic leaders, including House Budget Committee Chairman James Jones of Oklahoma and Ways and Means Chairman Dan Rostenskowski of Illinois, Reagan promised to coordinate with them on the tax and spending package now being drawn up by his economic team. Reagan also said he intends to address the nation "fairly soon" on the need to cut spending.

Apparently many decisions remain to be made. Reagan did not talk about the details of either tax or spending proposals and in fact spoke less than the others at the series of meetings, Jones said. These included David Stockman, director-designate of the Office of Management and Budget, domestic policy adviser Martin Anderson and Vice President George Bush.

In proposing that tax cuts be delayed, Greenspan, who spoke to reporters after testifying before Congress' Joint Economic Committee, has in mind such problems as the fact that actual tax withholding schedules affecting take-home pay cannot be altered until some weeks after a tax cut is ended. Making the cut retroactive, therefore, would require either making an extra, temporary reduction in withholding tax to compensate for over-withholding earlier in the year or paying large refunds the following year.

Making the cut retroactive to Jan. 1 and temporarily doubling the reduction in tax withholding after, say, July 1, would add about $7.5 billion to the fiscal 1981 deficit, estimated by the Carter administration at $55.2 billion compared with making the tax cut effective July 1. The retroactivity also would add a similar amount to the fiscal 1982 deficit.

If Greenspan's advice to delay is followed, Reagan officials also must make another choice about when to have the remaining installments of the 30 percent cut become effective. That choice, too, will have a considerable impact on the budget deficit in the short run.

The basic options are to get back on a calendar-year schedule by having a further 5 percent cut in rates as of Jan. 1, 1982, or wait until July 1 and cut rates another 10 percent. Either way, tax rates would be 15 percent lower in 1982, but having the earlier 5 percent cut would further increase the fiscal 1982 deficit.

If the first 10 percent cut is made retroactive to last Jan. 1, however, the remaining increments undoubtedly also would come on Jan. 1, 1982 and 1983.

Thus, Reagan could keep his campaign promise to cut personal income tax rates by 30 percent over three years but do so in a variety of ways. Choosing to have the cuts effective on three successive July firsts instead of January firsts could reduce the drain on fiscal 1982 revenues by at least $35 billion, a powerful argument for delay wholly aside from the technical problems cited by Greenspan.

Both Rostenkowski and Jones stressed their eagerness to cooperate with the new administration in the "tough months ahead," sources said. Rostenkowski gave Reagan some "advice from a veteran congressman" on the importance of consulting with Congress.

The need to raise the debt ceiling probably will be the first issue to come up in Ways and Means, sources said. Technically, the limit runs out on Feb. 28, but it will have to be dealt with before then.

Reagan told Jones he did not want to send piecemeal proposals to the Hill but would propose tax and spending measures together. Jones urged him to get support at grassroots levels for any spending measures. Without that, it would be hard to win support for real and deep cuts, he told the president, and if the proposals were defeated or cut back severely this would damage the chances of spending restraint in the long term.

Meanwhile, in appearances before the Senate Budget Committee and the Joint Economic Committee, several economists gave conflicting advice over whether major tax cuts should be enacted. Herbert Stein, Greenspan's predecessor as CEA chairman, told the Budget Committee taxes should be cut only to the extent that would be consistent "with the prompt achievement of a balanced budget in a desirable condition of the economy and with the proper defense expenditures."

Harvard economist Martin Feldstein said major spending cuts must be made, particularly in a variety of benefit programs including Social Security. He suggested modifying the annual cost-of-living increases for the next several years to eliminate a 20 percent across-the-board jump in benefits that occurred in 1972. Barry Bosworth of the Brookings Institution said that while there is no support for them at this time, wage and price controls could be used to cut inflation while keeping unemployment near 7 percent for several years.

All of the witnesses, including Greenspan, stressed that spending should be cut. Only Richard Rahn, chief economist of the Chamber of Commerce of the United States, gave tax cuts equal emphasis with spending cuts.