On the one hand, a Jackson candidacy would wipe away any realistic chance for Clinton to win a second term. Democrats don't win the White House these days without overwhelming support from black voters. They provided the winning margin for both Clinton in 1992 and Jimmy Carter in 1976, not just in several Southern states but in such Rust Belt states as Ohio and Illinois.
On the other hand, any action by the president seen as intended to placate Jackson could cost Clinton heavily among white working-class voters whose support he also needs in major industrial states.
What makes the Jackson threat so striking this time is that it seems to fly in the face of the new political reality of conservative Republican control of Congress and conservative domination of the Supreme Court on issues of importance to blacks.
And it is hard to imagine Jackson finding any of the potential Republican nominees for president preferable to Clinton on the issues that matter most to his core constituency. This is a field of candidates universally committed to ending affirmative action and cutting back on social spending. If any of them have any interest in saving the cities -- Jackson's declared priority -- it has been a well-kept secret.
But Jackson is unrelenting in applying pressure to Clinton. Asked in a televised interview the other night whether running as an independent might be "a better way to make your case" than to run against Clinton in Democratic primaries, he replied that such an option would give him "more time" to decide because the filing deadlines for primaries come months ahead of those for independent candidates.
Then he added: "I guess my first option is urging the president to honor his covenant and the economic stimulus promised for the cities, which is not there, some plan to reclaim our youth, some real challenges of pulling the nation together as we grapple with issues that have become quite divisive, like affirmative action. You can't duck those issues; you've got to tackle them."
Jackson's threat was explicit. "If that does not happen, of course, the primaries must be looked at," he said. "It's tough because he [Clinton] controls the apparatus. And perhaps the best way to get a permanent place at the table for workers, for cities, for those fighting for social justice is to open the process up [as an independent]."
But Jackson has to be aware that if Clinton meets his demands on affirmative action or in domestic spending priorities, he forfeits his continuing claim to be a "different kind of Democrat" -- the one he has reinforced with his decision to offer his own plan to balance the federal budget over the next 10 years.
The president's problem is complicated by the touchy relationship between him and Jackson. During the 1992 campaign, Clinton made a point of affronting Jackson when he attacked the rhetoric of rap singer Sister Souljah just as she appeared at a conference of Jackson's Rainbow Coalition.
The initiative paid huge political dividends. Culturally conservative Democrats in both the South and industrial belt -- the so-called Reagan Democrats -- saw the attack on Jackson as a refreshing contrast to what they had viewed as attempts by both Walter F. Mondale in 1984 and Michael S. Dukakis in 1988 to placate the civil rights leader.
But Jackson was outraged, and his anger was stoked by the way Clinton continued to keep him at arm's length at the Democratic convention and throughout the general election campaign. Nor has the breach ever been healed in Clinton's years in the White House.
In the past, Democrats believed that Jackson would eventually decide to stay within the party because what he wanted most was, as politicians like to say, "to be in the room" and have a seat at the table when major decisions were made.
Jackson has no such role today, and it is too late for the White House to offer him one, even if Clinton were so inclined, without being seen as capitulating to the crudest kind of political pressure.
The most vivid nightmare for Democratic leaders these days is Colin L. Powell on the Republican ticket next year and a defection of black voters en masse. But Jesse Jackson running as an independent could be equally fatal.