President Reagan last night vetoed a bill sharply limiting imports of textiles, shoes and copper, but he delayed the action until the last hour to avoid antagonizing House members whose support he was seeking on tax overhaul legislation.

The "damaging effects" of the import quota bill "would soon be felt by every American in the form of higher prices and shrinking economic growth," Reagan said in a draft of his message that circulated on Capitol Hill before he actually signed the veto shortly before 11 p.m.

A White House official said the president delayed the veto signing because "it would just cloud things up" to deal with a trade bill that had strong support in the Senate and House in the midst of the tax debate. The president faced a midnight Tuesday deadline for his veto.

The legislation had become the weapon for a bipartisan attack on the nation's trade deficit, which is expected to soar to a record $150 billion this year. Imports were blamed for factory closings and losses of manufacturing jobs, which supporters of the measure said had wiped out 356,000 jobs in the textile, shoe and copper industries.

The measure started as a bill to help the textile industry but was expanded in the Senate to include the copper and shoe sectors in an attempt to swell the number of supporters. It passed both houses by comfortable margins, but in neither case was the victory margin enough to override a veto.

The bill had bipartisan support, centered largely in the textile and apparel-producing states of the Southeast and the Northeast. Its major opposition came from lawmakers from farm states and export-oriented states of the Pacific Northwest, who felt their constituents would suffer most from retaliation.

Carlos Moore, executive vice president of the American Textile Manufacturers Institute, vowed the legislative battle would continue. "We are not going to go away," he said last night.

Shoe industry representatives were even angrier. "The Grinch who stole Christmas can step aside; today he has been replaced by President Reagan," said Carl Bontemps, president of the Footwear Industry of America. "The president's veto today makes a Christmas celebration highly unlikely for hundreds of thousands of footwear, textile and apparel workers whose jobs the president has just callously tossed away."

Sen. Strom Thurmond (R-S.C.) said, "The president heeded bad advice in vetoing the bill."

Despite the bill's strong support in Congress -- at one point more than half the Senate and two-thirds of the House had lined up as cosponsors -- a presidential veto was never in doubt. White House aides opposed the bill in Congress, calling it highly protectionist.

"It is my firm conviction that the economic and human costs of such a bill run far too high -- costs in foreign retaliation against U.S. ex-ports, loss of American jobs, losses to American businesses and damage to the world trading system on which our prosperity depends," Reagan said in his draft veto message.

Reagan threw a bone to the import-battered textile industry in his draft message while ignoring the complaints of shoe and copper makers.

He ordered Commerce Secretary Malcolm Baldrige to investigate textile industry charges that imports exceed the amounts allowed under international agreements. Moore said textile imports have doubled since 1980 and now account for 45 percent of American retail sales.

Reagan said he would tighten administrative and enforcement procedures if the industry charges are true.

The president also directed U.S. Trade Representative Clayton Yeutter to take a tough stand in negotiations that have just started for a new international pact covering trade in textiles and apparel called the multifiber agreement (MFA).

He said Yeutter should "vigorously pursue obtaining advantages for American textile and apparel firms" in both the MFA talks and bilateral negotiations with individual countries.

The bill would have rolled back textile and clothing shipments from the three leading suppliers -- Taiwan, South Korea and Hong Kong -- by as much as 30 percent. Shoe imports would have been limited for eight years to 60 percent of the U.S. market.