Across the sound, on Long Island, the Republican television ad portrays the Democratic congressman as one of the "Mondale Rockettes," kicking up his heels at the prospect of raising taxes.

Here, television viewers watch a poster of President Reagan being spattered with mud that the Republican narrator says is coming from the Democratic congressman who is fighting Reagan's economic policies.

This is the new form of "coattail campaigning," designed to defeat Reps. Robert J. Mrazek (D-N.Y.) and Bruce A. Morrison (D-Conn.) by linking them to Democratic presidential nominee Walter F. Mondale while their challengers latch onto the popularity of Reagan and his policies in their districts.

It may work -- but it hasn't yet. Private polls by both parties last week showed Morrison and Mrazek ahead although Reagan is far in front of Mondale in their districts.

But it is districts such as these that will decide GOP hopes of repeating 1980's top-to-bottom sweep.

Both Mrazek and Morrison are 40-year-old freshman Democrats who defeated pro-Reagan Republican incumbents by narrow margins in recession year 1982.

The ability of Democrats in districts like these to survive what they see as the approaching Reagan tide will determine whether Reagan can regain the working control of the House that he lost when Mrazek and Morrison were part of a 26-seat Democratic pickup in 1982.

Down in Washington, Martin Franks, director of the Democratic Congressional Campaign Committee, told reporters this week, "We can't see any evidence of coattails." He predicted that, "at worst, we will lose 10 seats."

But on the battlefronts in pro-Reagan suburbia, Mrazek and Morrison find it hard to take anything for granted.

"I don't think there are any coattails, either," Mrazek said after a League of Women Voters forum. "But it's obvious they are trying to turn this into a tag-team match in which I'm the bottom half of the Mondale-Mrazek team. I can't let that happen."

Both are doing what vulnerable incumbents always try to do to entrench themselves. They have taken advantage of the favorable committee assignments party leaders arranged for them -- Appropriations for Mrazek; Banking, Finance and Urban Affairs for Morrison -- to raise much more campaign money than they had two years ago.

But Mrazek's opponent, Robert Quinn (R), retired at 47 last year from Salomon Brothers investment banking firm and has loaned his own campaign substantial sums to try to win the seat. Morrison is in a rematch with former representative Lawrence J. DeNardis (R), who is as well-known in the district as the freshman incumbent.

Given Reagan's popularity -- recent polls put him 29 points ahead of Mondale in Mrazek's district and 26 points in Morrison's -- and the tiny margins they had in 1982, both men could be vulnerable to a national trend.

So they are trying to build a wall around themselves, stressing local-service aspects of their jobs and their accessibility to constituents.

At a candidates' fair in Huntington, where Quinn's table overflowed with Reagan-Bush bumper stickers, there was nothing with Mondale's name in the Mrazek booth.

But voters could learn from Mrazek's literature that he was "the hardest working congressman we've ever had," one who in just 18 months had gotten $23 million in federal funds to electrify the Port Jefferson branch of the Long Island Rail Road and "successfully lobbied the Appropriations Committee to provide millions of dollars in contracts for a score of smaller high tech firms on Long Island."

Here, Morrison opened his TV drive with a series of five spots in which constituents described the help he had given them and concluded in each instance, "Thanks, Bruce."

The former legal services attorney said his polls show that "what people really care about in their congressman is how he serves the district. The ombudsman factor is far and away the best predictor of how people will vote."

Challengers Quinn and DeNardis are doing their best to force the national issues to the forefront and especially to identify themselves as supporters of the Reagan economic policies their opponents fought.

"Bob Mrazek has moved as far away from the head of his party as he can get," Quinn said, "and tries to project himself as an independent. But he's voted 73 percent of the time against President Reagan, and if I beat him, I will defeat the biggest taxer and spender in the history of the 3rd District."

DeNardis, an organizer of the moderate Republican "Gypsy Moths" who dissented from some Reagan policies in late 1981 and 1982, now has tied himself tightly to the president.

"In 1982," De Nardis said, "he Morrison went after Reagan and me, saying that Reaganomics was a disaster. I'm not going to let him forget it this year."

But the Democrats have become adept at shifting the subject, and Republican professionals, such as DeNardis' campaign manager, Jamie Pound, concede that "so much of Reagan's appeal is personal -- the fact that people like his leadership style -- you just can't count on coattails."

Morrison said that in his own most recent poll, a 47 percent plurality of the voters agreed with DeNardis' contention that "Bruce Morrison has opposed Reagan's economic policies," but only 29 percent thought it was "very wrong" for him to do so.

Mrazek has even found a way to put a reverse spin on the Reagan coattails. Casting about for a way to dramatize the fact that Quinn has not voted in any state or local elections since 1980, he hit on a passage from a Reagan news conference urging all citizens to vote. The Mrazek ad plays a tape of Reagan talking about the duty to vote, and then says disapprovingly that Quinn "didn't bother to vote, but now wants to buy a seat in Congress."

If coattails can boomerang, Quinn has a real problem.