Opposition mounted yesterday on Capitol Hill to the Reagan administration's handling of tax exemptions for racially discriminatory private schools, and a Justice Department spokesman added fuel to the fire by saying department lawyers who protest the policy are "welcome to leave" the government.

Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) told White House officials that Senate Republicans are cool to legislation the administration has requested to restore the tax-exemption ban that it revoked earlier in the year.

"These people feel they don't need to pass a new law to say what's already on the books," said a Senate Republican leadership aide.

Baker said the administration was still pushing for legislation, which White House officials also asserted. But Baker said he would not rule out the possibility that the White House will eventually accept something less in the form of a resolution restating the policy against tax exemptions for discriminatory schools that had been in effect since the Nixon administration.

In the Senate, Baker added, "the preference appears to be for a resolution," although there is some difference of opinion about the form the resolution should take. "It may not be as united a position as it seems," he said.

Senate Finance Committee Chairman Robert J. Dole (R-Kan.), whose committee would handle any tax-exemption legislation, said he was among the senators who told Baker it would be "very difficult" to pass the administration's bill.

In the Democratic-controlled House, Speaker Thomas P. O'Neill Jr. (D-Mass.) took an even stronger position, asserting that neither legislation nor a resolution was needed or likely to pass the House to block the tax exemptions. "It's the law of the land," said O'Neill, referring to the 1964 Civil Rights Act and subsequent court rulings.

Moreover, said O'Neill, "We don't need a resolution . . . what's the purpose of a resolution?"

An aide to House Minority Leader Robert H. Michel (R-Ill.) said House Republicans are saying, "Let the courts decide the issue," meaning there exists no enthusiasm for legislation on the subject. "They feel it's been a mistake from start to finish. . . . Don't make matters worse by screwing around with it."

After granting a tax exemption to two all-white schools and getting hit by protests from civil rights advocates, the administration announced it would seek legislation to deny such exemptions, contending that existing law needed clarification.

The latest flare-up at the Justice Department came as chief spokesman Tom DeCair responded to a letter, signed by more than 200 of the civil rights division's employes, half of them lawyers, that said the administration's policy reversal "violates existing federal civil rights law, as expressed in the Constitution, acts of Congress and federal court interpretations thereof."

"Obviously when an administration changes as many policy directions as this one has, there are bound to be people who have been here awhile who may not agree. If they feel strongly about it, they are welcome to leave," said DeCair. Deputy White House press secretary Larry Speakes did not go as far as DeCair but said: "If they disagree it's up to them to decide what they wish to do." Added Speakes: "Once the president makes a decision he expects everyone to follow it. They can stay and hold opinions but the president expects them to support his policies."

William Bradford Reynolds, assistant attorney general for civil rights, also took a less caustic view of the protest than DeCair did. As he prepared to circulate among the protesting employes a copy of his legal justification for the policy change, Reynolds said he wasn't angry with the dissidents but added: "I wonder why they take that route. If they disagree and want to discuss things, that's healthy."