A rift with the White House over a controversial fund-raising letter has cost Republicans $2 million and forced a major cutback in money and services available to GOP senators, Senate aides were told yesterday.

The National Republican Senatorial Committee destroyed 8 million copies of the letter, produced at a cost of $2 million, after the White House objected to the prominent use of the name and photograph of Sen. Bob Packwood (R-Ore.), chairman of the committee.

The White House was upset with Packwood for telling an interviewer that Reagan was weakening the Republican Party by ignoring women and blacks and other minorities. He later apologized for the remarks.

This week, however, the outspoken Packwood was at it again, accusing Reagan of dividing the party by abandoning his campaign goal of balancing the federal budget. "He's removed the glue that held everyone together in the Republican Party," Packwood said in a Wednesday speech in Astoria, Ore.

GOP Senate aides said they were told yesterday that the campaign committee will have a cashflow problem for two or three months as a new letter is prepared and mailed out.

As a result, the committee has cut in half funds to individual senators for support services such as taping television spots and photographs of visiting constituents, according to spokesmen. It also has put a moratorium on hiring campaign consultants and drastically cut back on travel expenditures.

GOP aides were told about the cutbacks by Craig Smith, deputy director of the committee, in a meeting early yesterday. But there was already an undercurrent of unrest over the letter episode.

Phil Kent, press secretary to Sen. Strom Thurmond (R-S.C.), had circulated a letter to other GOP press secretaries urging them to mount a lobbying effort against the cutback in support services funds, which are allocated to each senator in proportion to his state's population.

"I don't have to point out to you how critical these funds are to our communications with our bosses' constituents," he said.

The meeting with Smith caused more uncertainty among top Senate aides, who came away with differing accounts of how much the controversy over the letter would cost.

Bob Pipkin, spokesman for the committee, said the only direct cost will be the $2 million lost from the letters because of White House objections.

Although it will delay fund-raising efforts to from six to eight weeks, he said the committee hopes to eventually recoup its losses. The committee, he added, still hopes to funnel more than $10 million into the campaigns of Republican senatorial candidates this year.

"Fortunately, we were in such dramatically better shape than the Democrats that this won't hurt our candidates," Pipkin said. "This isn't something we take lightly, but we can deal with it."

The letter--promising medallions and American flags to big contributors--were written over a facsimile of President Reagan's signature. "As your president, I am calling upon you to make a most unusual sacrifice . . . a sacrifice for your country--in order to keep our Republican majority status in the Senate," the letter said.

Reagan, however, didn't write the letter or authorize the use of his signature, according to White House spokesmen. Packwood and other committee members agreed to withdraw the letter in a hastily called meeting two weeks ago. About 2 million letters already had been mailed