[sonofagun]

In order for a Bill to become law, it must be signed by the President

Ten days after presentation of the bill to the President, if the president does not veto the bill, the bill becomes law.

So, no, the President doesn't have to sign it.

How does the court deal with a fraudulent President?

It may be that, say, the Health Care bill is deemed to have never been signed by a legitimate president and so became law after ten days.

[Smokin' Joe]

I believe the Bill has to be presented so the President has the opportunity to veto it. If there is no President, that has not been done and the conditions are not met. Handing the Bill to the maid would not have been sufficient.