That may have been true before the 17th amendment where the state governments could choose senators who would respect states' rights. Now the only real power the states can exercise over the federal government is the power to call a Constitutional convention with the aim to reconfigure or even dissolve the current federal government just as they did in 1787 with their "few modifications" to the Articles of Confederation. That isn't merely playing with fire, it is juggling nitroglycerin.
What about each state passing some kind of recall mechanism? That way they could recall senators who do not stand up for their states.