WASHINGTON — Could David Duke hurt President Bush's hopes for reelection?Mr. Duke, a Louisiana state representative, this week became the first prominent figure to challenge George Bush for the 1992 Republican presidential nomination. Another well-known conservative, Patrick Buchanan, is expected to enter the fray next week. "Government has increased continually under the George Bush administration," Duke told a jam-packed press conference where he announced his candidacy. "Taxes have increased. The massive government bureaucracy has gone on and on. And the middle-class taxpayer is not getting any sort of relief.... I believe very strongly that we need a change." Duke compared his long-shot bid to Jimmy Carter's successful campaign in 1976. But if he falls short, Duke said he may throw any Republican convention delegates he wins toward "alternative candidates" to Bush, if any emerge. Analysts suggest that Duke does pose a potential danger to Bush, however, especially if he later launches a third-party campaign. Even if Duke's support in a general election were small - perhaps 3 percent or 4 percent - that could be enough to tip certain states like Illinois, Pennsylvania, and New York into the Democratic column. Duke's appeal is especially strong among middle-class white voters who are suffering in the current recession. In last month's Louisiana governor's election, he took 55 percent of the white vote, but still lost because the minority vote was strongly against him. Many of those white voters for Duke supported Ronald Reagan and George Bush in the past three presidential elections. Duke, a former grand wizard of the Ku Klux Klan and a former Nazi sympathizer, opposes foreign aid, demands that welfare recipients work for their checks, urges incentives to discourage illegitimate births, and supports prayer in schools. In addition, Duke urges sharp restrictions on immigration. He charges that immigrants are adding to unemployment, crime, and welfare costs, while damaging the environment with overcrowding. Duke predicted he will do especially well in the Texas primary, where immigration could be a major issue.