Senate Republicans, eager to capitalize on President Reagan's strong showing in opinion polls, are pressing him to make a big pitch for GOP Senate candidates this fall in hopes of enlarging the party's 10-seat majority and shoring its defenses against a major Democratic assault in 1986.

Sen. Richard G. Lugar (R-Ind.), chairman of the National Republican Senatorial Committee, told reporters at a breakfast meeting yesterday that several long-shot Republican challenges could turn into close races with a strong "coattails effect" from Reagan's reelection effort.

Lugar mentioned races in Nebraska, Montana and Michigan, where Republican challengers are trailing but closing the gap, as examples of contests that could turn on how Reagan fares.

Lugar reiterated that he expects the GOP to hold its current 55-to-45 Senate margin after the election Nov. 6, although he said a gain or loss of three seats is possible.

With an extra push from Reagan resulting in more than 55 GOP seats, he added, "we'd make great headway in retaining control in 1986," when many of the seats gained by Republicans in Reagan's 1980 sweep are expected to be in jeopardy.

Republicans will be defending 22 of 34 seats at stake in 1986, an even higher percentage than the 19 of 33 being defended this year. Moreover, some incumbents seeking reelection in 1986 are considered highly vulnerable.

In addition to seeking an extra boost from Reagan to help build a cushion for 1986, Lugar said the committee hopes to raise enough money this year to assure the maximum allowable contribution to 1986 candidates as well as those running this year.

Democrats have contended that Reagan's popularity is basically personal and may not be transferable to other Republicans, although they have expressed anxiety recently about whether Democratic congressional candidates might suffer unless there is some improvement in the campaign fortunes of presidential nominee Walter F. Mondale.

In a state-by-state analysis, Lugar indicated that Republicans might lose a seat from Tennessee while picking up one from Massachusetts. He characterized races in North Carolina, Iowa and Illinois as close but said there are substantial and "widening" margins in other once-threatened states such as New Hampshire, Minnesota, Mississippi and Texas.