Even in BUsh thought the case against Obama had merit, why would he do otherwise? Can he rule on the matter? Unless something happens quickly, Obama will be our next President, even if he is a fraud.
The President could direct the Attorney General to join the lawsuits, or initiate one in an appropriate Federal District Court. There are probably laws against fraud in federal elections. There are certainly enough federal laws concerning elections, one of which is bound to cover fraudulently running for federal office, possibly raising campaign funds based on fraud.
Futher he could direct the FBI to investigate to find other indications of BO's ineligibility, or eligibility for that matter.