The federal budget resolution that congressional conferees approved this week divided not only Republicans and Democrats but at one frenzied point late Thursday had the White House and State Department at odds over cuts in President Reagan's foreign policy programs.

Early in the week Reagan had said in letters to GOP congressional leaders that the cuts could "cripple" U.S. interests in the Middle East, Europe and Africa. But by Thursday he had agreed reluctantly to compromise on reductions after Senate GOP leaders and presidential lobbyists informed the White House that cuts could not be avoided.

That did not stop State Department lobbyists from swarming around the conferees to argue against the $600 million cut in foreign assistance the conferees ultimately approved. The lobbyists circulated the Reagan letter and "talking points" they had prepared but not cleared with either the White House or the Office of Management and Budget.

These contradictory efforts angered some in the White House, although OMB Director David A. Stockman yesterday shrugged off what he described as State's "unilateral initiative," saying, "There may have been a few company commanders who were behind the curve."

The conferees' adoption Thursday night of a $11.5 billion ceiling on foreign operations in fiscal year 1983 set off a scramble in Congress yesterday over how the cuts are to be absorbed and resurrected the possiblity that no foreign aid legislation would pass this year.

"Something has to give," said one Senate aide, wondering how to accommodate a budget ceiling that is $600 million lower than a bill approved by the Senate Foreign Relations Committee.

The administration reluctantly agreed to the House-Senate compromise on foreign affairs as the price of getting any budget resolution passed--and only after the president had pleaded in vain for the Senate-approved ceiling of $12.1 billion.

In a letter to Senate Budget Chairman Pete V. Domenici (R-N.M.) Tuesday, Reagan strongly argued that only an acceptance of that level would provide funds for his administration's objectives.

Accepting the House version, which is $860 million lower, Reagan warned, "could have far-ranging effects that could cripple us" in several areas. He cited this country's ability to play peacekeeper in the Middle East, to negotiate for military bases in Spain and Portugal, and to provide military assistance for countries such as Pakistan, Oman, Kenya and Tunisia.

The conferees' ultimate compromise was $262 million higher than the House-favored mark. In a telephone call to Domenici Thursday night, Reagan said he would accept the lower figure if necessary to get a budget resolution that would pass.

Foreign aid is so unpopular in the House this year that even that modest compromise may be in trouble there.

Finding room for the cuts poses major problems for House and Senate committees. If across-the-board cuts are made, the normal rule calls for using either the president's requested figure or the current fiscal year's level, whichever is lower.

By one estimate prepared in the House yesterday, that could result in a cut of up to $450 million in Mideast aid programs, largely from those promised Egypt and Israel. However those programs are strongly supported by powerful lobbies and by the administration, which considers them part of the assistance needed to preserve the Camp David peace process.

It is more likely, some sources predicted, that the cuts will be taken from such programs as Food for Peace, the Peace Corps and some State Department operational funds.

One administration paper drafted for the budget talks concluded that even if the higher Senate mark were approved there would be "Draconian cost-saving measures" required within the department, including the "closing of many consulates."