Eugene notes the interesting question of whether a state could pass an advisory recall of a Senator. As I discussed in one of my papers on the 17th Amendment (see this article, pages 171-173 especially) for the Framers the issues of “instruction” and “recall” were tied up together. Under the Articles of Confederation, state legislatures had the power of both instruction and recall. Under the Constitution, however, state legislatures continued to exercise the power of instruction, but no longer had the power of recall for failure to follow instructions. Senators were understood as being “ambassadors” of the state to the national government, thus it followed that they could be instructed.
The absence of a power of recall was a major sticking point for the Anti-Federalists, who anticipated that without the power of recall, the power of instruction would be largely a dead letter. My recollection–although I can’t at the moment place my hands on the source–was that there was a major showdown over instruction at the time of the Andrew Johnson impeachment, and that (if I recall correctly) at least one Senator resigned rather than voting to convict Johnson, as he had been instructed by the state legislature.
I’ve seen nothing in the history of the 17th Amendment that would suggest to me that the power of instruction and advisory recall was changed by the 17th Amendment. My reading of that history is that the 17th Amendment was designed to primarily just change the mechanism by which Senators were elected, but not to change the traditional idea that Senators were fundamentally ambassadors of the state. Of course, changing the mode of election has fundamentally changed the relationship between Senators and their electors, but based on my reading the legislative history of the 17th Amendment, I suspect that the sponsors of the amendment would have been surprised at the way in which the Senate as a political body has evolved into just another version of the House. My sense is that they thought that the norm that the Senate was a representative of the states in their corporate bodies was so deeply-rooted that merely changing the mode of election would have little effect, an assumption on which they were clearly incorrect.