WASHINGTON--The Senate approved, 63-36, and sent to the White House a sweeping trade bill yesterday, but supporters fell short of the two-thirds victory margin needed to override a threatened presidential veto.

"The minuses outweigh the pluses," Sen. Orrin Hatch (R-Utah) said after the vote. He called key plant-closing provision that drew heavy fire from the Administration "economic terrorism."

Democrats tried to win over at least 14 Republicans and thus gain a veto-proof margin. They ended up with 11 GOP senators while losing one Democrat, retiring Sen. William Proxmire (D-Wis.), who was conerned about the bill's changes in the Foreign Corrupt Practices Act.

The Reagan administration lobbied until the last minute to avoid a recurrence of its defeat last week when the House passed the trade bill by a margin large enough to override a veto.

One wavering Republican who supported the bill the first time around, Sen. David Karnes (R-Neb.), went to the White House and met for 30 minutes with President Reagan, Vice President Bush, chief of staff Howard Baker, Treasury Secretary James A. Baker III and Energy Secretary Donald Hodel.

He emerged from the session expressing concern over duty-free imports of ethanol from the Caribbean and saying "what I needed was the president's assurance that the Administration was going to introduce another bipartisan bill that could be quickly passed by the Congress and signed."

"And I think he has done that," Karnes said.

Reagan renewed his veto threat and promised to work later for a milder version in a letter Tuesday to Senate Minority Leader Bob Dole of Kansas.

Reagan called on lawmakers to "finish the trade bill process in a way that serves America's interests--not the special interests."

Most Administration fire has been directed at a provision that would require all but the smallest companies to provide their employees with 60-day notice of plant closings and largescale layoffs.

Sen. Edward M. Kennedy '54 (D-Mass.) defended the embattled plant-closing provision, saying 40,000 plants have shut down in this decade of increased foreign competition.

"Nearly 2 million people have lost their jobs each year," Kennedy said. "Yet the Administration does not want workers to know their jobs are in danger and to have time to plan for new ways to provide for their families."

The Administration dangled the prospect of a slimmed down version of the bill, minus the plant-closings and perhaps other provisions, once Congress has sustained Reagan's expected veto of the current measure.

But Democratic leaders said this could be the last chance to support trade legislation before the fall election campaign.

The House passed the bill last Thursday, 312-107, more than the two-thirds margin needed to override a veto.

The bill would overhaul the system under which the United States imposes import curbs and takes other steps to retaliate against international trade violations.

Authority to retaliate would be transferred from the president to the U.S. trade representative. Retaliation would be mandatory, but the bill provides five broadly phrased exceptions, such as threats to national security.