COLUMBUS, OHIO — COLUMBUS, Ohio -- When you ask Joel Hyatt, the Democratic nominee to fill the U.S. Senate seat being vacated by his retiring father-in-law, Howard M. Metzenbaum, whether he wants President Clinton to campaign for him this fall, Hyatt unsmilingly says only, "We'll see." This cool reaction to the prospect of having the president of the United States speak in your behalf is heard increasingly around the country as Clinton's popularity limps along. But it is particularly notable in a state where the president himself has such a clear stake in having a Democrat hold the Senate seat and where Hyatt is the underdog. The Republicans regard the Ohio race, in which their candidate, Lt. Gov. Mike DeWine, leads Hyatt by 44 percent to 33 percent in the latest Akron Beacon Journal poll, as perhaps their best shot to win an open Senate seat now held by a Democrat. It is basic to their hopes of gaining Senate control with a pickup of seven seats -- and making Clinton's next two years a nightmare. Aides to Hyatt suggest he has a particular problem with a campaign visit that goes beyond Clinton's current standing in the polls. One of the loudest arguments against their candidate's first try for public office is that he hopes to get elected on the coattails of his father-in-law, who is stepping down after 20 years. To blur the charge, Metzenbaum is not campaigning for Hyatt, although he has raised money for him. "At a time we're keeping Howard out of the race so the Republicans can't say he's trying to hand the seat to his son-in-law," says Dale Butland, a Hyatt aide, "we have to indicate that Joel is running on his own." Hyatt himself says: "I don't think coattails will determine the outcome. I can't do it by proxy, whether it's President Clinton, John Glenn [Ohio's other senator] or Howard Metzenbaum. It's my challenge to meet." However, others in the state think that coattails will be critical -- for DeWine. He is running as the unabashed helpmate of very popular Republican Gov. George V. Voinovich, who is seeking re-election and leading his little-known Democratic challenger, state Sen. Rob Burch, by 61 percent to 12 percent in the same newspaper poll. DeWine boasts that because he has overseen seven Voinovich administration agencies involved in fighting crime and drugs, he is justified in cashing in on the governor's popularity. Hyatt, noting that crime remains the No. 1 concern of Ohio voters, says: "I'm not sure he ought to be bragging about the job he's done." In a race in which the "coattails issue" is so prominent on both sides, DeWine's campaign manager, Barry Bennett, insists that Clinton is an indirect factor favoring DeWine whether he campaigns for Hyatt or not. He cites a Dayton Daily News poll in which voters said they preferred experience to a new face. "Two years ago it would have been just the opposite," he says. "Everyone voted for change. We elected someone [Clinton] who we didn't know at all, and now we're not too happy about it. "In this election, voters are going to make their decision not on what promises were made, but what promises are kept." Prior to DeWine's present job, he was a congressman for eight years, a state senator and a county prosecutor. This experience contrasts clearly with Hyatt's attempt to start out in politics at a very high level, feeding the notion that his father-in-law is trying to hand the seat over to him. Ohioans, Bennett insists, "want an election, not an ascension." Hyatt is bucking another handicap as a "television lawyer." He is well-known for his ads selling low-cost legal services, but "lawyers are right down there [in public esteem] with politicians," Butland says. DeWine also is a lawyer, but doesn't have as high a profile as one. One rap against DeWine is that he's a perennial candidate, having run for five different offices in the past six years. Although he is clearly a conservative, he is accused by an independent candidate, abortion foe Joe Slovenec, of being a "moderate," and Slovenec could cut into his conservative vote in a close election. At the same time Hyatt, like Metzenbaum a liberal but less categorically so, hopes to pin the tag of right-wing extremist on DeWine, a strong Reagan-Bush supporter in Congress. But in the end, personal connections -- DeWine with Voinovich, Hyatt with Metzenbaum, and Clinton -- could determine who is Ohio's next senator.