Chairman Bob Packwood (R-Ore.) abruptly postponed a Senate Finance Committee vote on President Reagan's proposal for a free-trade agreement with Canada yesterday to save the administration from a defeat that the president said could hurt U.S.-Canadian relations for years to come.

Delaying the ballot until today may have allowed the president to pick up the votes he needed, although committee members were uncertain which senators would switch sides.

Reagan faced strong committee opposition for a variety of reasons that had little to do with the free-trade pact with Canada. Sen. John C. Danforth (R-Mo.) was particularly angry over what he saw as the administration's refusal to deal with Congress on a trade bill, while other members were upset over regional trade frictions with Canada involving products such as lumber, potatoes, fish, cattle and hogs.

Danforth proposed a 30-day delay to give the White House time to explain more fully its aims on the Canadian pact and to work with Congress on overall trade legislation.

Sen. William L. Armstrong (R-Colo.), who reportedly received two phone calls yesterday from Reagan seeking his support, was angered over the administration's refusal to stop imports from the Soviet Union that he said were made by slave labor.

"We are now at the back-room, closed-door, arm-twisting stage," said Sen. Max Baucus (D-Mont.), an opponent of the measure who warned of a "stench" from the deals the president would strike to get the needed votes.

"It's leverage time," U.S. Trade Representative Clayton Yeutter said as Packwood ended the committee hearing. "We've got a lot of work to do, obviously."

Yeutter was acting as point man for administration efforts to win "fast-track" authority from the committee to negotiate a free-trade pact with Canada. This procedure allows Congress only to approve or disapprove a completed agreement, without the possibility of making any changes in it. The Senate Finance and House Ways and Means committees, which hold primary jurisdiction over trade, have until today to vote against "fast-track" authority; otherwise, the president gets the authority automatically.

Danforth, the leading opponent, said the measure would have been defeated, 11 to 9, if Packwood, a supporter, had allowed a vote. Majority Leader Robert J. Dole (R-Kan.), who was trying to manufacture a compromise that would give the president the needed votes, agreed that the free-trade pact likely would have lost.

"It was close, but no cigar, this morning," Danforth said. Later, he said he doubted his slim majority would last the night.

In statements yesterday morning, nine committee members indicated they supported the president, while eight said they opposed him. But the three who declined to announce their position before the vote, including Armstrong, were considered to be in the "no" column.

Most committee Democrats, along with Danforth and Sen. John C. Heinz (R-Pa.), lined up against the measure, while most Republicans, along with Democratic Sens. William Bradley (N.J.) and Daniel Patrick Moynihan (N.Y.), supported the president.

"If there is any country in the world we ought to be able to conclude a favorable free-trade agreement with, it is Canada," Packwood said. Earlier this month, Packwood led off a firestorm of criticism from committee members that first told the administration the pact was in trouble.

Sen. Steven D. Symms (R-Idaho) also switched from his position of a week ago, when he wrote the president he opposed the agreement. He said Reagan had assured him the administration would forcefully pursue an agreement with Canada that would help U.S. lumbermen hurt by Canadian imports.

Dole, who also signed a letter last week urging the president to withdraw his proposal, was another vote-switcher. In an effort to gain votes for the president, he promised to bring broad trade legislation to the floor as soon as the Senate finishes tackling the budget.

As majority leader, moreover, Dole offered a possible compromise that included guidelines for the administration in negotiating the agreement, but Danforth called the proposal "waste paper." Baucus and Sen. George Mitchell (D-Maine) questioned the value of presidential assurances on specific issues.

The issue driving Danforth and Sen. Lloyd Bentsen (D-Tex.) was the administration's refusal to deal with the Senate on trade legislation. Danforth accused the administration of considering Congress as "dirt under its feet in international trade."

"The basic position of the administration," he continued, "is, what they want in international trade is what they should get, no questions asked, and our role is just a rubber stamp."