The House Education and Labor Committee gave formal approval yesterday to President Carter's proposed expansion of the government's college tuition grant program - paving the way for a floor vote on the legislation, possibly later this month.

The bill, approved 32 to 3, would provide for somewhat larger tuition grants than Carter proposed for middle-income families, and would eliminate the President's proposal to limt students-loan guarantees to families earning $40,000 or less.

At the same time, the measure would give congressional appropriation committees a choice between a financing level that would hold to the $1.2 billion extra that Carter has proposed and a slightly more generous version that would boost that by $200 million.

The more expensive version would allow larger grants for students in all income brackets and would extend at least some scholarship aid to those whose families earn up to $25,000. The grants provided in the less-costly measure would go only to families earning $23,440 or less.

The action puts Carter's scholarship aid plan a small step ahead of the rival tuition tax-credit peoposal that it is designed to replace. With yesterday's approval, the scholarship bill is ready for floor action in both the House and the Senate. The tax-credit bill is on tap only in the Senate.

Carter has lambasted the tax-credit legislation for including benefits for families of elementary and secondary school students. The administration contends the tax measure would cost too much and give private schools an unfair advantage over public schools.

The two rival measures are in a neck-and-neck race in both houses, with billions of dollars riding $4.5 billion when fully effective, compared to $1.4 billion for the scholarship plffective, compared to $1.4 billion for the scholarship plan. Catholic school forces are supporting the tax-credit bill.