A House-Senate compromise on controversial college tuition tax credits came apart yesterday, and the bill - that President Carter has threatened to veto anyway - may not be dead for this Congress.

Conferees had agreed earlier on a bill to help defray the costs of attending college, but not private elementary and secondary schools, as Catholic educators wanted. The House Thursday night unexpectedly rejected this plan.

To placate the House, the conferees voted yesterday to contend the credit to offset schools, as Catholic educators wanted. The House Thursday night unexpectedly rejected this plan.

To placate the House, the conferees voted yesterday to extend the credit to offset secondary school costs as well, leaving out elementary schools.

But the Senate is considered unlikely to accept this proposed extension. For one thing, many senators think aid to Catholic and other sectarian elementary and secondary schools would be unconstitutional.

Rep. Barber B. Conable (N.Y.), the top House Republican on the conference panel, said he would try to retain the tuition credit proposal as part of the general tax out bill, which also is in conference.

But Sen. Russell B. Long (D-La.) and Rep. Al Ullman (D-Ore.), chairmen of the two congressional tax-writting committees, hinted they would not fight hard to keep the provision in the big tax bill. As a result, its prospects seemed doubtful for the session.

The developments came as the formal conference on the general tax cut bill was temporarily suspended yesterday as House and Senate Democrats met privately in separate groups to work out proposals for a compromise version of the bill.

The conference committee canceled morning and afternoon sessions while House Democrats huddled with Treasury Secretary W. Michael Blumenthal and other administration officials. Insiders reported progress was slow.

Meanwhile, Carter warned he was vigorously opposed to a Democratic version of the Republican Roth-Kemp tax cut bill added on by the Senate this week. Carter said he might veto the tax cut bill if the provision survives.

Sponsored by Sen. Sam Nunn (D-Ga.), the amendment would slash income taxes by $142 billion, or 5 percent a year, from 1980 through 1983, provided the government can meet stringent targets for holding down federal spending. The targets are vitually unattainable, many experts believe.

Jody Powell, Carter's press secretary quoted the president as saying the Nunn amendment "in its present form . . . is not workable or acceptable." Powell said the provision was pass "in haste" and could prove to be inflationery.

The combination of actions appeared to heighten the confusion surrounding the end-of-session work on the tax cut bill, dimming prospects that the lawmakers will be able to complete the bill before their scheduled adjournment today.

The conferees are trying to reconcile a $16.3 billion tax cut bill passed by the House and a $29.1 billion Senate bill that is $1.2 billion over the budget in the current fiscal year alone.

The move by the Democrats to meet only in closed-door caucuses appeared to mark an attempt by conference leaders to take the decision-making out of the spotlight in an effort to hasten an agreement.

However, the ploy drew fire from Republicans, who were left out. Cona-allowed to participate" in drafting the compromise bill.

Because of Conable's objections, House Democrats later agreed to allow the House Republican conferees to join the discussions.

By early evening, the House conferees had decided on only one major provision that Carter had cited as crucial - a Senate proposal to roll back a key portion of the 1976 Tax Reform Act dealing with taxes on the sale of inherited property.

The 1976 law contained a provision that would have raised taxes on the profits from the sale of inherited property by heirs - a "loophole-closing" provision hailed at the time by "tax reform" advocates.

However, the Senate voted - and the House conferees agreed informally yesterday - to put off the measure for three more years, effectively shelving it permanently. Carter has said repeatedly that rolling back the 1976 provision would heighten prospects of a veto.

In the conference on the tuition tax credit bill early yesterday, House representatives ran into opposition from Long, who warned that the Senate already had rejected the notion of extending the writeoff to parents of private and parochial elementary and secondary students, and would not alter its stand.

By late yesterday afternoon, the Senate still had not voted on the House compromise to allow the credit only for private and parochial high schools, and not for elementary schools, and Senate leaders showed no signs of pressing for a quick vote yesterday or today.

If the Senate were to accept the House proposal, the measure could be shoehorned through at the end of the session. If not, however, it would die unless it is retained as part of the overall general tax cut bill.

However, Carter has warned repeatedly he will veto any bill that contains the tuition credit legislation. Long told the conferees yesterday he did not think Carter was bluffing.

The compromise the House conferees offered the Senate was to allow the tuition tax credit of 35 percent of costs and fees of college students and private and parochial high school pupils, up to a preset maximum.

In the case of colleg students the maximum writeoff would be $100 this year $150 in 1979 and $250 in 1980. For high school students, the maximum would be $50 this year, $100 in 1979 and $150 in 1980.