Can the governor retain the Democrats' solid black support while appealing to white voters who have abandoned the party in part because they perceived it as too closely bound to black interests?
While his centrist strategy certainly could work, it is risky, especially because the race has narrowed, as expected, after last week's Republican convention.
Several factors work in the governor's favor. For one, Jesse Jackson is not as singular a figure in black politics as he was in 1984 and 1988, and no matter how faint the praise, he has endorsed the Clinton-Gore ticket.
Moreover, Mr. Clinton's positions are entirely consistent with black opinion.
A recent poll by Home Box Office and the Joint Center for Political and Economic Studies found broad black support for virtually all of his positions, including the death penalty and welfare reform.
In addition, black voters have compelling reason to vote this year for reasons other than the presidential race and most will choose Mr. Clinton over President Bush when faced with the choice.
There are a dozen new black congressional districts and at least 80 new black state legislative districts, most in the South.
Governor Clinton's strongest black support in the primaries was in the South, where three-fifths of black voters live. He has considerable rapport with Southern blacks and support of black political leaders there.
The turnout among Southern blacks should be helped by get-out-the-vote drives in the re-election campaigns of five senators in four states.
Richard Shelby of Alabama, Bob Graham of Florida, Wyche Fowler of Georgia, John Breaux of Louisiana and Terry Sanford ** of North Carolina were all elected six years ago with substantial black support.
Another advantage for Mr. Clinton is that black voters will remain Democrats.
While attachment to the party is weakening among younger blacks, overall support remains in the mid-80 percent range.
But Mr. Clinton cannot afford to assume that he has the black vote sewed up. Outside the South, his black support in the primaries was not especially strong.
His share of the black vote in four key states was 20 percent to 30 percent below his Southern share: California (61 percent), Maryland (49 percent), New Jersey (64 percent) and New York (52 percent).
Overall, black turnout in the Democratic primaries was down substantially from 1988. An HBO-Joint Center Poll, taken before Ross Perot withdrew, found only 43 percent support for Clinton nationally.
Thus, 57 percent did not support him, including 20 percent undecided and 11 percent "none of the above."
Before he was nominated, Mr. Clinton dismayed many black Americans, especially outside the South, with a series of "gaffes," calculated or not. These included golfing at an all-white country club and embarrassing Mr. Jackson by choosing to criticize Sister Souljah at a Rainbow Coalition meeting to which he had been invited by Mr. Jackson.
The governor's response to the Los Angeles riots was no more dynamic than Mr. Bush's.
The major black figures in a future Clinton administration have not yet emerged. Though he has been endorsed by most black politicians, there is no widespread sense that these leaders are insiders or Clinton intimates.
Black activists and voters might wonder who will staff a Clinton presidency.
Mr. Clinton should take a hard look at the Bush White House's black appointments -- Colin Powell, Louis Sullivan, Ed Perkins (United Nations), Constance Newman (Office of Personnel Management), Arthur Fletcher (U.S. Commission on Civil Rights), Condoleezza Rice (ex-National Security Council) and Walter Massey (National Science Foundation).
The Arkansas governor has prepared for divisive Willie Horton-like attacks from the Republicans, but he might consider that he has protected himself too much.
While the number and percent of black delegates declined at the Democratic convention in New York, there were 107 black delegates in Houston, a 75 percent increase from 1988.
No one expects black Americans to turn to Mr. Bush in any significant numbers. Black voters appreciate the necessity of following one's head rather than one's heart.
But in the absence of clear sign that he genuinely welcomes their votes and that his administration would attend to their concerns, Mr. Clinton risks losing the substantial black support he will need on Election Day.
In a memorable gesture John F. Kennedy called Coretta Scott King after her husband had been jailed in 1960.
Mr. Clinton should reflect on how he might demonstrate his intentions to those who do not yet recognize him as a friend.
David Bositis, senior researcher at the Joint Center for Political and Economic Studies, is co-author of the forthcoming "Politics and Linkage in a Democratic Society."