Even if they did, would it be illegal? They were not trying to influence Sestak's actions as a member of the House. They were trying to influence his actions as a private citizen who was deciding whether to run for the Senate. I know that is a very fine point, but most government corruption laws are about trying to influence someone in their position as a government official. I don't know if offering a non-civil service government position to someone would be illegal.
Several days ago, Judge Napolitano laid out the cites, I'm sorry, I have not his brilliant legal mind or ability to retain, but in essence he said it violates the law because the president or those under his authority could make good on the offer, that was the bar, legal hurdle crossed. Different from typical political maneuvering, shenanigans. It is illegal to bribe someone in this manner. If I can find the specifics for you, I will post them.
Sestak case deepens--did White House commit a felony by offering a job to Sestak?
The Judge's comments:
Well the ramifications are potentially enormous. I mean to offer someone something of value in order to affect their official behavior as a member of Congress is a felony. We call it a bribe. To offer someone something of value to affect the outcome of an election is a felony. Each of those carries five years with them. The government has an affirmative obligation to investigate this.And Congressman Sestak who is a decent guy, we've all interviewed him. He sent you handwritten thank you notes after he was on your show, whether he agrees with you or not. Congressman Sestak has an obligation to tell the truth. Who offered him a job? What was the quid pro quo and what was the job? If he doesn't say that voluntarily a federal prosecutor should bring him before a grand jury and the grand jurors will inquire of his knowledge as we like to say.
Read the whole page, there's more information included in the quoted exchange. The part about having the ability to make good on the offer is left out here, but I recall the Judge making a strong point of that.