The founders wanted the President convicted in an impeachment only if there's a 2/3 vote in the Senate. Do you think a simple majority of voters in favor of that conviction should be enough to trigger 2/3 of Senators to be and vote likewise in favor?
I don't think Senators should vote based on what a majority of voters thinks, and certainly not when that majority is as doubtful as it is here, where the only safe conclusion from looking at the polls is that it's too close to be sure which side has the majority.
Meanwhile, there are definitely more than 34 Republican Senators (maybe as many as 50!) who know that they are gone if they vote to convict on the charges the House has come up with so far, and likewise would be doomed if they side with the Democrats to expand the investigation in the Senate, essentially giving the prosecutors a do-over on constructing their case.
Impeachment goes nowhere unless polling shifts dramatically, right? Polling only shifts dramatically if some super-damning new evidence is found. Seems unlikely.
I agree with basically all of this except the first sentence. How weak or strong the House's case was is really quite immaterial. It clearly could have been stronger if they had taken more time to build their cases and had waited to see if they could enforce subpoenas through the courts. Or if Trump had been even more blatant about abusing taxpayer money for his private purposes. But we all know that it's not how strong the case is, or how flagrantly Trump violates the law, that is the deciding factor. It's purely a question of whether he alienates enough of his supporters as to allow Republican Senators the necessary breathing room to vote independently.
And regarding vulnerable Republicans not daring to vote with the Dems to expand the investigation in the Senate - I don't know, I could see a scenario happening where witnesses are in fact called, for instance if the Democrats agree to have Joe Biden as a witness as well. Would make sense to me.