Republican congressional leaders said yesterday they plan to build a $13.5 million war chest to help the party strengthen its control of the Senate and take over the House in the 1982 election.

Sen. Robert Packwood, chairman of the National Republican Senate Campaign Committee, predicted the party will pick up at least two or three seats in 1982, and perhaps as many eight or nine. His committee hopes to raise $25 million, $8.5 million of which would go directly to candidates, to help this effort.

"There is not a single Democratic senator who is not vulnerable," the Oregon Republican said.

The Congressional Republican Campaign Committee, meanwhile, has approved a budget of $20 million for an unprecedented off-year effort in 1981, and hopes to have from $4 million to $5 million on hand to donate to candidates the following year, according to its chairman, Rep. Guy Vander Jagt (Mich.).

The most visible part of his program will be a multimillion-dollar television advertising blitz this spring to help President Reagan sell his proposed budget and tax cuts, he said. House Republicans have approved an initial $2 million for the commercials.

The House group has put together a nine-member field staff to work with state legislatures on reapportionment. The committee is also increasing its candidate training effort, studying the records of Democrats whom it considers vulnerable in 1982, and advising the 52 new Republican congressmen elected last fall on how to respond to counterattacks from Democrats.

Traditionally, the party of a sitting president suffers election losses in non-president years. But both Vander Jagt and Packwood, in separate sessions with reporters, expressed confidence that Republicans can not only avoid those losses in 1982, but register gains. Their optimism has been fueled by a series of post-election polls conducted for the two committees.

Among the poll findings:

GOP House candidates actually collected more votes than their Democratic counterparts in 1980, although they won only 41 percent of the seats.

Sen. Daniel Patrick Moynihan (D-n.y.) may be in trouble. One Republican poll after the election found that 25 percent of the state's voters, including many Democrats, planned to vote against him in 1982. The same poll found Moynihan trailing former representative Elizabeth Holzman in a Democratic primary trial heat by a 38 to 43 percent margin.

Voters considered GOP candidates equal with Democrats in such human characteristics as trustworthiness and competence in 1980. As late as November 1979, Republicans trailed Democrats by a margin of 18 to 43 percent in these areas.

Voters generally accepted the Republican theme "time for a change."

Although they conceded the economy will play a key role in 1982, Packwood and Vander Jagt argued that a complete economic turnaround isn't necessary for Republican success. "The key to success is to show improvement," said Vander Jagt. "You don't have to solve the problem. You simply have to show enough improvement to give people hope."

During the last two years, the House Republican campaign committee raised $27 million, and the Senate committee $20.5 million. Their Democratic counterparts raised $1.65 million and $2 million.