Remember the post "California legislators ask Mexican Senate to intervene [in driver's licenses for illegal aliens]"?

I don't know if those requests crossed the line. Perhaps they were legal, or perhaps not. From the U.S. Code:

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.

This page talks about citizen diplomacy when normal talks have broken down, but I don't think that applies in this case.