Highly doubt it; while a 'majority of the majority' of the Committee on the Judiciary might be in favor of impeachment, there's a permanent contingent of moderates and leadership-Republicans who will oppose it, and whatever the tactical benefits of a serious Obama impeachment attempt, no Democrat can support it at any point in the process, which is what it would need. Now, is a Bush-'07 style attempt possible? Yes, though I doubt even that would occur. But Democrats have been salivating at the mouth about a Clinton-'98 style attempt since 2011; they need to get over that it won't be happening unless some more substantial scandal erupts.
Individual Republicans, of course. The Republican Leadership, of course not.
The Republican Leadership is weak. If the hard-rights wants a vote on impeachment of the President then they will get one.
End of the shutdown? Sandy funding? Pretty sure every time the right has tried to fight the leaders, the leaders have won.