The controversial tuition tax credit bill faces its first major test in Congress today as the House begins floor action on the measure. A close vote is predicted on the key issue of whether to extend the break to private and parochial school pupils.

After weeks of delay, the House is scheduled to start debate on the measure late this afternoon, with prospects of passing the tax credit legislation sometimes tomorrow. The bill has become one of the hottest tax issues in Congress.

Approval of the legislation would give the tax credit measure a head start over President Carter's rival plan to increase federal scholarship aid for middle-income families. Carter has told House leaders he would veto the tuirion credit bill.

Both sides are predicting an unusually close vote, particulary on the critical question of whether to allow the tuition credit for elementary and high school pupils in private or parochial schools. With many members still home in their districts, voting is expected to be light.

The House also is scheduled to vote on whether to increase the size of the tax credit. The bill drafted by the House Ways and Means Committee would allow taxpayers to reduce their taxes by up to 25 percent of tuition expenses, to a maximum of $250 by 1980.

Rep. Charles Vanik (D-Ohio: has proposed a floor amendment that would increase the tax credit to 50 percent of tuition costs. However, it is not certain which the House may vote on the issue. Opponents argue that any increase would bloat the budget deficit.

The tuition tax credit proposal has gained popularity over the past several months, primarily as a from of middle-income tax relief. The bill was introduced last year mainly to help offset rising college costs, but Catholic groups have sought to extend it to parochial schools.

Carter tried last winer to prevent enactment of the tax credit measure by proposing instead a $1.46 billion increase in existing federal college scholarship programs. The adminstration had criticized the tax credit approach as too costly and inefficient.

However, lobbing by parochial school groups has intensified support for the tax measure. Despite Carter's threat of a veto. House members refused eariler this year to consider the president's plan without first voting on the tax credit legislation.

The rival approaches also are running neck and neck in the Senate, where both bills have gone through committees and are ready to be sent to the floor. The Senate temporarily has shelved the measures to work on labor law "reform."

Amendments extending the tax break to elementary and secondary school pupols and increasing the size of the creit are among three floor votes to be allowed on tomorrow. The other involves a separate tax-deferral plan by Rep. Abner Mikva (D-I11.).

Mikva's plan would allow parents to defer payment of up to $1,000 a year of their federal income taxes - to a maximum of $6,000 - to cover college costs. In effect, the tax deferral would be a form of loan. Taxpayers would repay the money over 12 years at 3 percent interest.

The move to extend the aid to parochial school pupils has stirred a bitter debate over the past several weeks. State and local school officials have contended that subsidizing private school tuition would exacerbate the exodus from public schools.

The Ways and Means Committee measure would cost just under $1 billion when fully effective in fiscal 1981, compared to $1.4 billion for Carter's plan and $4.5 billion for a Senate version that would include private and parochial schools.

The tax credit to be voted on by the House tomorrow would become effective next Aug.