Majority Leader Robert C. Byrd said Friday he was not sure the bill overhauling America's trade laws would pass the Senate by the two-thirds majority needed to override a threatened presidential veto.

But Byrd said President Reagan, when deciding whether to veto it, should not presume the Senate could quickly strip out provisions opposed by the White House and pass another version.The trade bill, the result of a House-Senate compromise between competing versions, rolled through the House on Thursday by an overwhelming 312-107 vote.

"The administration ought to pay close attention to the whopping majority of that vote," Byrd said. "I think the House vote will give added momentum" to its supporters in the Senate.

Byrd said he could "only hope" that if Reagan vetoed the bill, the Senate could find the two-thirds majority needed to override. The president's lobbyists were working hard against it, he said.

If the president's veto were sustained and the Senate forced to bring forward a new bill, it would have to re-run the "obstacle course" the current compromise has already cleared, he said. The president should assume "this is it it won't get another chance," said Byrd, D-W.Va.

"I sincerely hope . . . that in the end the president will sign the bill," Senate Finance Committee Chairman Lloyd Bentsen, D-Texas, said Thursday.

Byrd said the Senate would begin debate on the bill Friday and a vote was expected next week. He said Republicans assured him it was unlikely opponents would try to tie up the legislation with a filibuster.

Byrd again warned that an administration favorite the pending free-trade agreement to phase out tariffs between the United States and Canada could get entangled in any Reagan veto.

Reagan said Thursday that he will veto the bill if it arrives on his desk with a provision to require all but the smallest employers to give 60-day notice of plant closings and large-scale layoffs.

Business groups have fought the plant-closings provision on grounds it would dry up capital for investment, frighten off customers and cause economic stagnation.

Unions are calling for the measure, saying that notifying employees about to lose their jobs is the only humane thing to do.

In recent days the dispute over plant closings has overshadowed the centerpiece features of the bill, which would streamline the system under which the United States aids companies threatened by imports and retaliates against international trade violations.

A key vote in the House came just before the roll call on final passage, when lawmakers voted 253-167 against a move by Minority Leader Robert H. Michel, R-Ill., to send the measure back to conference committee with orders to drop the plant-closings provision.

On the final vote on the bill itself, the hefty House margin reflected concern in Northeastern states over import competition and perhaps election-year reluctance to fight anything billed as sharpening the U.S. edge in global markets.