On one level, this whole caper has blown up in Trump’s face, unified a formerly divided Democratic Party into launching a formal impeachment inquiry, divided Republicans, and cost him in the polls.
On another level, you need to squint pretty hard at the polling data thus far to see the impact. His poll numbers sunk a point or two when the Ukraine news initially broke but seem to have rebounded back as the impeachment process went on. Looking at Trump’s approval as a whole, his two worst moments were the unpopular 2018 tax law and the government shutdown in early 2019. Nothing that’s come out about Ukraine has been nearly that bad for his approval numbers.
And in a larger sense, to the extent that Trump’s goal was to hurt Joe Biden’s presidential prospects, his strategy is arguably working. Biden’s approval ratings, after all, have declined over the past several months more clearly than Trump’s have. Then again, all the main Democratic presidential candidates have suffered from declining approval numbers during the course of the campaign, so Trump’s actions may have nothing to do with that.