First, for context, I believe the GOP as a party would be better off with a swift impeachment and resignation than a protracted scandal. Every week this remains in the news, their ability to pass legislation is impaired, and the GOP’s risk of losing the House in 2018 goes up. When you have a festering wound, sometimes the best thing to do is to accept the pain of cauterizing it, quickly. However, I see very few signs of it happening.
The problem is this. Trump’s support is still high among his base. His popularity is likely extremely high among the minority of GOP voters who vote in the primaries. That means that any GOP House member who voted to impeach would be at major risk of losing to a Trump loyalist in the 2018 primary. Thus, no individual House member can dare be too aggressive without risking their seat.
A legislator can only move forward if they believe that the GOP’s base has or is imminently about to turn against Trump, thus protecting them from losing out to a more conservative opponent in the primaries.
Trump’s support among his base has to fall substantially before that can happen. There’s no sign of that happening any time on the horizon.
Or, of course, GOP Reps could vote to impeach if their conscience demanded it, at the risk of losing their seat. That’s possible. But I’d put the odds against it.