Could run through the American court system if federal prosecutors decide to bring charges against Nancy Pelosi for her blatant disregard for American law and the U.S. Constitution.

The Logan Act:

"Any citizen of the United States, wherever he may be, who, without authority of the United States, directly or indirectly commences or carries on any correspondence or intercourse with any foreign government or any officer or agent thereof, with intent to influence the measures or conduct of any foreign government or of any officer or agent thereof, in relation to any disputes or controversies with the United States, or to defeat the measures of the United States, shall be fined under this title or imprisoned not more than three years, or both.

This section shall not abridge the right of a citizen to apply himself, or his agent, to any foreign government, or the agents thereof, for redress of any injury which he may have sustained from such government or any of its agents or subjects."

Article II of the Constitution assigns international diplomacy to the executive branch. And, Article I mentions nothing about diplomacy under the Speaker of House duties and responsibilities.

But, let's not allow Madame Speaker to go to court alone. The way I see it, she should have plenty of company in the courtroom if feds appropriately bring up charges against the congressmen that accompanied her on the trip:
David Hobson (R-OH)
Keith Ellison (D-MN)
Tom Lantos (D-CA)
Henry Waxman (D-CA)
Louise Slaughter (D-NY)
Nick Rahall (D-WV)
Frank Wolf (R-VA)--led a previous unauthorized delegation

For the record, I do not agree with the President's Foreign Policy techniques. I think we should always keep communications open with these countries. But, there is a legal and constitutional way to pressure the President to adjust his foreign policy. Going in to Syria and meeting with one of the greatest state sponsors of terrorism and telling him that the road to peace will come through his country, on a trip that is unauthorized by the U.S. State Department is a blatant disregard for American law, borne out of complete arrogance and dismisiveness toward an equal branch of government.

How can the Democrats complain about Bush's disregard for the other branches of government when Pelosi's disregard is no different?

[UPDATE 4:39 PM]: The Wall Street Journal originally introduced the idea of prosecution under the Logan Act. Here is their article on the subject: http://opinionjournal.com/extra/?id=110009908