Zero chance in Senate.
It's zero chance until the electoral consequences get bad enough for Senate Republicans, at which point they will abandon him, like they did Nixon. The way this story is progressing, with the staggering incompetence of Trump's team, it's looking more likely than ever. It's still not looking very likely, mind, but this has ten times the legs the Russia thing ever did.
If nothing else, this hurts Trump's re-election chances. It might not convince any of his hardcore base, but he needs more than his hardcore base to win in 2020. He can't afford this.