CINCINNATI -- When George Bush reversed his stand on new taxes, the response was simple for many Republicans seeking congressional office this year: Establish distance from the president and keep up the door-knocking.

But for three black candidates recruited by the national GOP to run for congressional seats in Ohio, Kentucky and Connecticut, the potential complications run far deeper.

In Ohio, J. Kenneth Blackwell, a former Cincinnati councilman and mayor who is seeking to succeed retiring Rep. Thomas A. Luken (D), drew fire from the local NAACP for supporting Bush's veto of the Civil Rights Act of 1990 this week. In Kentucky, J. Alfonso Brown, a Louisville businessman who has never before sought public office, has objected to the president's civil rights stand and favored abortion rights. And in Connecticut, Waterbury alderman Gary Franks is hoping to defeat Democratic comeback candidate Toby Moffett in a district that is just 4 percent black.

Brown's battle against seven-term incumbent Romano L. Mazzoli is the toughest of the three. The Ohio and Connecticut races for two open seats are considered tossups.

None of the three likes to talk about race as a factor in the election, but if any of them wins, he will be the first black Republican to serve as a voting member of the House since Illinois's Oscar DePriest was defeated in 1934.

Any victor is also destined to become the prize example of what the Republican Party likes to call its outreach strategy, an effort to broaden the party's base to include minority voters.

Housing and Urban Development Secretary Jack Kemp, now the administration's chief ambassador to traditionally non-Republican urban areas, said a victory would be a "sharp signal of the inclusiveness of the Republican party."

Blackwell, Franks and Brown are dealing with challenges that have lately grown more complicated as Bush, whose popularity was once unrivaled, especially among black voters, has begun to sink in the public's estimation. A slumping economy, Kemp added, "certainly hurts our chances."

For Blackwell, 42, on whom the party's brightest hopes are pinned, the campaign has been an inside-the-Beltway roadshow. Bush has visited twice; Barbara Bush once, and Kemp has twice come to Cincinnati on his behalf. He is also the conservative's conservative: On the desk at his suburban campaign headquarters, he keeps three cassette tapes of speeches by Rep. Newt Gingrich (R-Ga.), and quotes him frequently on the stump.

Blackwell is hoping to convince voters that his opponent, Cincinnati Mayor Charles Luken, the incumbent's son, has inherited his father's insider status to such a degree that voting for Luken would be an endorsement of everything that's wrong in Washington.

Luken in turn disparages the national GOP's high-profile support for Blackwell, saying that his candidacy has been "propped up by the celebrity du jour." As a result, he said, Blackwell would be more loyal to his party than to his district once in Washington.

Face to face at a community debate last week, the two were cordial and exchanged quips about the times they worked together in city government. But in a Luken television ad, Blackwell's photograph is flip-flopped as a narrator describes his defection from the Democratic Party by saying: "It seems there are so many Ken Blackwells running for office."

Blackwell served as Kemp's deputy undersecretary for intergovernmental relations until earlier this year and shares many of his views. He recognizes the distance Republicans have to go.

"The president's support within the African-American community is probably one mile long and two inches deep," he said. "It's very, very fragile."

Louisville's Brown, who is the only black Republican struggling to unseat a Democratic incumbent, copes with this dilemma daily. On one day last week, he made a campaign pitch to a white fraternity alumni luncheon. An hour later, his aides were pointing out proudly that a group of local black Baptist ministers had endorsed him. Brown has papered his district with billboards showing him with a smiling Bush, but he sent the president a telegram last week objecting to the civil rights veto.

Although Bush has stumped for Blackwell and Franks, he has not campaigned for Brown. Barbara Bush came to Kentucky for Sen. Mitch McConnell's reelection campaign, but Brown was not on the podium. And when Vice President Quayle toured a senior citizens home with Brown, he offered an offhand one-sentence endorsement before rushing off to give a speech and play a round of golf.

Brown's ads portray him as a hurdler who has overcome great obstacles. Of the three black Republican candidates, only Brown describes himself as moderate rather than conservative. He also praises the value of pork barrel spending in Congress. Louisville, he said, is the "worst-funded congressional district in the United States of America."

Brown also seems aware of GOP vulnerability in this fall's elections and has lately been keeping his distance from the party. "The message is, you need to vote for the man, for the individual," said Jay Humbert, a Brown aide.

To win, Brown is counting on two-thirds of the Republican vote, half the black vote and three-quarters of voters who favor abortion rights. Mazzoli is antiabortion.

Brown is also hammering away at Mazzoli, but on the same themes the incumbent has faced and managed to turn back from nearly every challenger he has defeated. Last week, the Louisville Courier-Journal endorsed Mazzoli, the insider, over Brown, the novice.

The road appears far less rocky for Franks. Moffett, who lost his congressional seat in a failed 1982 Senate bid, has raised twice the money Franks has, but Franks has generated favorable notices.

"He's received more attention nationally for being a black potential history-maker than he has here in the fifth district," said Stephen Beaujon, Franks's spokesman.

Franks, 37, who owns a realty firm, has sought to label Moffett a carpetbagger who moved into the district just in time to run for the seat being vacated by Republican gubernatorial nominee James G. Rowland.

The election of any of the three black Republicans would alter the makeup of at least one long-standing Capitol Hill institution: the 24-member, all-Democratic Congressional Black Caucus, which has not had a Republican presence since Sen. Edward W. Brooke (R-Mass.) was defeated in 1978.

Blackwell appears to relish the chance to crash the party. "I just figure there will be a whole lot of minority reports written," he said.