The best thing Republicans in Congress can do is to give the President and Democrats their head. Let them pass their destructive agenda without a single "NO" vote. Vote "Present" on every issue.
Sure, go ahead and present our vision and our proposals in Congress--Go the the public and tell them:
"We get your message and we are going to do exactly as you have voted. We don't agree with the agenda and we have alternative proposals and beliefs, but we will not stand in the President's or the Democrat Congress' way. Just be warned that their way will lead to disaster . . . and that we do have alternatives which will work."
Then sit back and allow the nation to reap their rewards. The lesson would be worth the damage.