The Washington Examiner Editorial Board thinks he should. I am not so sure, at least for his 2008 election campaign. But if executives have to give back bonuses because they are funded by taxpayer bailouts, then Obama should not take campaign contributions for executives of companies the government bailed out with taxpayer money. That would be like taxpayer funded campaign contributions.
On the other hand, it could a back-door way to the beginning of taxpayer financed political campaigns.