The Senate Finance Committee shrugged off pressure from the White House yesterday on tuition tax credits as a majority voted for a strong anti-discrimination amendment opposed by the administration.

Chairman Robert J. Dole (R-Kan.) warned that giving the Internal Revenue Service authority to enforce anti-discrimination portions of the bill would "doom" the measure. He said he would not move it to the Senate floor with the amendment attached.

The committee also voted to cut the maximum allowable tax credit in 1985 from $500 to $300, to phase out the tax credits for gross adjusted incomes in the $40,000-$60,000 range, and to allow refunds to low-income persons who pay too little in taxes to qualify for a full tax credit.

In a dramatic session full of arm-twisting, behind-the-scenes conferences and shifting votes, the debate centered not so much on the desirability of tuition tax credits as on how to make sure they aren't awarded to parents who send their children to racially discriminatory schools.

Senators of both parties complained about leaving enforcement solely to the Justice Department, and only at its discretion. The White House yesterday sent up a package of strengthening amendments which were quickly adopted. But Sen. Bill Bradley (D-N.J.) asked for an even stronger provision to allow the Internal Revenue Service to share enforcement power. Bradley said the IRS routinely audits the schools anyway and might uncover evidence of discrimination before a formal complaint was filed.

The administration has refused to go along with the Bradley amendment on the grounds that the IRS has sometimes been overzealous and could revoke a school's eligibility even if no complaint has been filed.

Under the new White House language, schools would be required to include a statement in all published materials and in an annual oath to the IRS that they do not discriminate. Any individual could file a complaint against a school with the Justice Department. The department would be required to file suit if it found merit in the claim. Individuals could also file suits. To recover eligibility for tax credits, schools would have to prove in court that they no longer discriminate.

Last January the administration changed its position on a decade-old IRS policy of denying tax exemptions to schools that discriminate. The president said the IRS did not have authority to revoke the exemptions on racial grounds. Widespread public outrage prompted the administration to introduce legislation to restore the IRS powers. The matter is now before the Supreme Court.

Dole cautioned the committee that the tax credit bill is supported by a "very fragile coalition" that would fall apart if the Bradley amendment was adopted.

William Bradford Reynolds, head of the Justice Department's Civil Rights Division, charged that Bradley's amendment "invites the IRS to establish procedures to go in and audit schools..., inviting some kind of ill-defined participation by the IRS in the private schools' activities."

On the first vote, the Bradley proposal lost 10 to 9, with two Republicans, John C. Danforth (Mo.) and John H. Chafee (R.I.), voting with a majority of the Democrats in favor of it.

As the committee was winding up, Sen. Bob Packwood (R-Ore.) called Dole to complain that his proxy was recorded as no when he meant yes. The vote switched to 10 to 9 in favor of the Bradley amendment.

The vote became 10 to 8 when another Republican, Sen. David Durenburger (Minn.), called to withdraw his proxy vote against the amendment.

After the Bradley amendment passed, Dole proposed a compromise that would postpone any tuition tax credits until a law is passed to make sure they don't go to schools that discriminate.