The legisl00tures could, apparently, successfully pressure the Sinators to resign, however. (Yes, I spelled it that way on purpose.)
Not exactly. The men chosen as senators were part of the state's political establishment and were good at reading the tea leaves. Legislatures did not need to pass resolutions to "instruct" a senator how to vote, although some did. A guy didn't get to be senator without understanding how his state's politics worked.
There was no need to pressure a senator to resign. If he wasn't welcome anymore, he would know it without being told.