I suspect that Obama wants the 'pubs to push impeachment. If that had been on the table for this past election, he would've used it to rally the base. "Those evil 'pubs want to impeach the first black president". He didn't get that issue, instead he got a "Ferguson Effect" where people voted against Obama's lawless agenda, and he went down in flames far more than it seemed possible.
If stopping the invasion of the US is framed by expressing how the current policy is destroying opportunities for minorities and other entry-level US citizens, how it's diverting resources away from communities, and how it's a cheap trick by the Chamber of Commerce and other corporate interests, stopping the invasion will be impossible to ignore by elected pols, both parties.
Instead, we've got RINO backstabbing corporate profit globalists having their way. If we should impeach anyone, it's them, if they yet again turn their backs on the voters who gave them another chance to save the US. This time, they have more constitutional conservative voices in the HOR and US Senate to deal with, so we can hope.