And while prosecutors have brought increasing numbers of political corruption cases in recent years, they have done so using laws that make it a crime for an official to deprive the public of “honest services.” The cases are based on statutes that never define exactly what conduct might be illegal and do not require proof of a bribe or a quid pro quo to establish criminal wrongdoing.

Image The case against Gov. Rod R. Blagojevich, shown outside his home on Monday, may turn out to be difficult to prosecute. Credit... Joshua Lott for The New York Times

What those statutes do require is evidence that an official at least tried to seek something of value in return for an official action.

In the case of Mr. Blagojevich, it would be legal for the governor to accept a campaign contribution from someone he appointed to the Senate seat. What would create legal problems for him is if he was tape-recorded specifically offering a seat in exchange for the contribution. What would make the case even easier to prosecute is if he was recorded offering the seat in exchange for a personal favor, like cash, a job or a job for a family member.

Indeed the government has claimed the wiretaps show that Mr. Blagojevich told his aides that he wanted to offer the seat in exchange for contributions and for personal favors, including jobs for himself and his wife.

But talk is not enough. Any case will ultimately turn on the strength of the tapes, and whether the governor made it clear to any of the candidates for the Senate seat that he would give it only in exchange for something of value.

Several lawyers cautioned that the complaint presented last week was a snapshot of the evidence that Mr. Fitzgerald had amassed so far, in an investigation that is continuing.

In moving to arrest Mr. Blagojevich on Dec. 9, Mr. Fitzgerald acted without having presented his case before a grand jury. He is now likely to use such a panel to obtain additional witness testimony exploring whether anyone, including anyone in the Obama camp, had specific discussions with the governor’s office about filling the vacancy.