The Federal Election Commission has well-defined rules limiting how much any given individual or PAC may contribute to a federal candidate's campaign. Some entities, such as corporations, are forbidden from donating at all. The chart below is from the FEC web pages relevant to the issue.
With regard to paying down Senator Clinton's primary campaign debt, the key take-away points from the chart are that a campaign acting honestly cannot accept more than $2300 per individual, even if the individual is one's wealthy spouse - indeed considering the media scrutiny of FEC reports, I would say ESPECIALLY from one's wealthy spouse. One candidate's committee may give another's up to $2000. So, Barack Obama and Michele Obama can (and have) jointly contribute $4600 to Senator Clinton's primary campaign and Barack Obama's primary and general election committees could each donate $2000 to Senator Clinton's primary campaign (I do not know whether Obama's authorized campaign committees have made these contributions. Note too that Joe and Jill Biden can give $4600 and Joe Biden's authorized campaign committees can give $2000 per committee.
What is most striking about this chart, however, is that there is NO LIMIT on how much an authorized candidate committee can give to a national political party or state or local parties per year. So President-elect Obama's authorized campaign committee could simply pay off the DNC's debt and urge individuals to pay down Senator Clinton's primary debt rather than urge them to pay off the DNC's debt. Senator Obama could also organize a PAC or several PACs, each of which could give $2300 to Senator Clinton, much as Hillpac raised money for a variety of Democrats and donated to their campaigns (as a multicandidate PAC, Hillpac was permitted to contribute up to $5000 to any other candidate running).
Now, I have no doubt that there are ways to skirt these rules and regulations but not to the extent where Bill Clinton or Barack Obama can simply write a check to Hillary Clinton For President (Senator Clinton's primary campaign committee) for 8 million dollars. Also, while a candidate can loan or contribute any amount of money to her own campaign, nobody may contribute "through another", so Bill Clinton cannot simply transfer money in his name to Senator Clinton which she can then turn around use to pay the primary debt. I do not know whether funds held jointly by the Clintons, if indeed they do hold funds jointly could be used to do this, although my intuition would be no.
Now, none of this means that any rank and file voter in this country is obligated to contribute or contribute again to pay down Senator Clinton's primary debt. I understand that in an ever worsening economy people are certainly disinclined to do so, and that various people have other objections to doing so.
The interesting question is whether, if Senator Clinton is debating whether to accept a position in an Obama administration, she will - to the extent legally permissible - condition her acceptance on firm guarantees of fundraising assistance from President-elect Obama's top donors. We will certainly never know if this issue is part of the discussions between Senator Clinton and President-elect Obama but I would certainly hope so.
My own position continues to be that if you can spare a contribution to pay off the debt, it is worth doing so as an act of camaraderie not so much with Senator Clinton but with all the millions of Americans who object to the way the DNC treated her candidacy, her supporters, her delegates, and the nominating convention in Denver. A simple donation of $5.51 (the 51 cents standing for the percentage of women in the American population) would serve that purpose. And the elimination of Senator Clinton's debt before the elimination of the DNC's serves the further purpose of making it clear that while you may care for certain Democrats you have decided you will not let the Democratic Party take you for granted. In short, for $5.51 you can gain a sense of self-affirmation and do something proactive at a time when the the Democratic Party as an institution seems oblivious to the fact that in winning the Presidency they lost the confidence and trust of large parts of their traditional constituencies. If you are so inclined, you can make this statement by contributing for the express purpose of retiring Senator Clinton's primary debt right here.