Democrats' impatience with whip cracking from the Reagan administration began to surface yesterday as party leaders in both houses of Congress warned the administration that it must supply more information on its tax- and spending-cut proposals before Congress can respond.

In the strongest statement thus far on administration efforts to whip up public support for speedy action on its economic package, the House Democratic study Group accused the administration of pressuring Congress to act on proposals that are "vague, incomplete [and] confusing" and of "hampering efforts to obtain more complete information."

The sharpness of the DSG attact contrasted with the honeymoon-period gentleness with which the established Democratic leadership in the two houses has handled its relations with the new Republican administration.

But yesterday both House Speaker Thomas P. O'Neill Jr. (D-Mass.) and Senate Minority Leader Robert C. Byrd (D-W.Va.) -- while still avoiding direct criticism of Reagan -- agreed that he has yet to give Congress the kind of specific information it needs to start drafting legislation.

Congress has so far gotten only "generalities" to back up "gloom-and-doom" warnings from Reagan about the consequences of inaction, said O'Neill. "The committees and the Congress won't buy a pig in a poke," added Byrd.

Nonetheless, Byrd joined O'Neill and Republican leaders in both houses in agreeing to a legislative timetable under which both the tax-cut and budget-cut packages could be enacted by mid-summer. Byrd also said he thinks that Reagan's proposal for program cuts sufficient to save $125.9 billion over the next years, including $41.4 billion in fiscal 1982 presented a "useful target."

The DSG, which started as a liberal instrument but now represents most Democrats in the House, said the administration has supplied inadequate backup information on the proposed spending cuts, no details on relaxation of regulations, skimpy data on the implications of price decontrol for oil and natural gas, little if any supportive material on its proposals to consolidate grants programs for health, education and social services, and no details on new defense spending proposals, foreign aid cutbacks, and changes in black lung benefits.

The DSG acknowledged that the administration has promised to supply many of these details by March 10, but its chairman, Rep. William M. Brodhead (D-Mich.), complained that "the administration makes a mistake by making members targets of mail campaigns and by sending Cabinet officers out to pressure for quick action before giving us even the most elementary details of its proposals."

Brodhead and the DSG also accused the Departments of Labor and of Health and Human Services of imposing a "gag rule" on officials to preventng them from responding to congressional inquiries unless authorized by "political appointees."

A Health and Human Services official said such a directive had gone out but added that it is similar to directives issued during the Carter administration.