Yes, its possible the House could try to impeach Trump using any number of reasons. But politically the reasons would have to be something very substantial which would attract Senate repos in voting Trump guilty. I haven't seen or heard of anything, so far, which fit this scenario.
In my opinion this is more in line with Clinton's impeachment than with Nixon. Keep in mind the impeachment of Clinton was a repo failure and probably cost them more than they gained in pursuing it.
From what I've heard many demos secretly oppose impeaching Trump as far as what is known today. They believe, like the repos against Clinton, it could cost the demos more than they gain. My take is the demos will continue the political theater which includes threatening to impeach but will not impeach.