It doesn't matter, as they're using that narrative already. You're right in that the best way to combat Trump is to bury him through the voting booth, but those Trumpistas are coming out to vote no matter what. What are they going to do with a knife-in-the-back narrative, vote harder?
Democrats need to forget about polling, stop worrying about what the Senate will do, and defend the Constitution as is their sworn duty. The whole argument for impeachment is that the POTUS has acted outside the bounds of the Constitution. With ample evidence to indicate his transgressions, Congress is shirking their duty if they fail to impeach. Plus, once impeachment hearings are opened, I assume it will be easier to get key players, e.g., Mueller, to testify before Congress. That will create an environment in which more Senate Republicans will be pressured into defecting back into reality.