Impeachment would only make a martyr out of him. To many on the left, especially the blacks, would see it as “getting the black man”. It would reinforce the mantra that it was his color all along.
The Republicans have enough information on him now to put behind the scenes pressure on him and if only one state demands a long form BC enough pressure would be applied that he would just slither away. That could be used to show that he just wasn’t up to the job and didn’t have what it takes to lead.