There were people standing by Nixon until the bitter end. (And probably think fondly of him today if they’re still around.) Approval ratings aren’t going to save anyone if they’ve broken the law.
Pardons can save lots of people, though, and a high enough approval rating leads to a removal-proof and even investigation-proof Senate.
The Senate can also do a lot more damage than failing to act, too. After all, what prevents the Senate from opening a select committee investigating Robert Mueller’s involvement in killing Vince Foster? The same thing that prevented the Benghazi hearings–the lack of enough chutzpah to carry out an obviously political show trial. Don’t think they won’t.