Congress yesterday began knitting together 1,943 pages of House and Senate trade legislation into a seamless bill, an alteration job expected to involve as many as 180 lawmakers in one of the largest and most complex legislative conferences on record.

Only 81 lawmakers -- 44 from the Senate and 37 from the House -- were named to the conference in time for its opening, a largely ceremonial meeting in the Cannon House Office Building's caucus room, one of the few facilities big enough for such a massive negotiating session.

House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) said that as many as 100 more House members will be needed to tailor the legislative fabric by the time the conferees get to work in earnest after Labor Day.

Staff members of the 12 House and nine Senate committees were instructed to begin putting together detailed comparisons of the bills passed earlier this year by the House and Senate.

The conference will have to tread a narrow line between meeting the congressional objective of passing a tough trade bill that hits unfair trade practices -- which are seen as hurting U.S. companies -- and being labeled protectionist by the White House, thereby drawing a veto. The bills passed the House and Senate by overwhelming bipartisan majorities, but the Democratic leaders of Congress are unsure if they can hold on to enough Republican votes to override a veto by President Reagan.

As set up by the Democratic leadership, the conference will be largely under the control of Rostenkowski, who was elected conference chairman, and Senate Finance Committee Chairman Lloyd Bentsen (D-Tex.), who was elected cochairman. While their committees have primary jurisdiction over trade, members of the other committees with jurisdiction over parts of the bill will also be included.

Administration officials are convinced that the portions of the House and Senate bills under jurisdiction of the Ways and Means and Finance Committees can be worked into legislation acceptable to the White House. But they are concerned about the parts approved by other committees, including a House section they feel would restrict needed foreign investment and a portion in the Senate bill that would force large companies to give notice of plant closings and mass layoffs.

There is suspicion on Capitol Hill and among certain business groups that some administration officials prefer that no trade bill be signed because any measure would depart from the president's free trade philosophy, which has been softened over the past two years under pressure of record trade deficits.

Both Rostenkowski and Bentsen promised in their opening statements to work with Reagan in writing legislation that he can sign, but warned that the president will have to exhibit flexibility to meet congressional aims.

"All parties will have to compromise," said Bentsen.

Rostenkowski urged the president "to refrain from further veto threats" and suggested that one of his major trade initiatives -- global trade talks to strengthen the compact that governs world trade, the General Agreement on Tariffs and Trade -- "will wither for lack of congressional support" if the trade bills are not enacted into law.