Efforts to deny tax exemption to segregated private schools should have little trouble winning support in the US Senate.
President Reagan, acting in the face of criticism on almost every side except the most conservative, has asked Congress to pass a law forbidding tax exemption to schools that discriminate by race. On Jan. 7 he lifted an Internal Revenue Service antidiscrimination rule, thus opening the door for segregated private schools to gain tax exemptions.
He can be assured of Democratic as well as Republican support for the aim of his bill, proposed this week, to reinstate the antidiscrimination by congressional action.
''I am pleased to see that the President has responded to the pressure exerted by Congress and the American people,'' said Sen. Gary Hart (D) of Colorado, in response to the Reagan bill.
Senator Hart is leading a group of 30 cosponsors who are pushing for a similar measure. A spokesman for Hart says that his bill will be much like the President's proposal, although it will include a direct swipe at the President's IRS action. The Hart bill will state that existing tax law already forbids tax subsidies for schools that discriminate.
The President's proposal would apply retroactively back to 1970. However, it would still leave the question of whether schools that claim to discriminate based on religious belief are entitled to tax exemption. The legislation would allow exemptions for such schools only if they have ''an exclusively religious curriculum.''