No.
The House can impeach, but no one can put together 67 Senate votes to convict, not going to happen.
It’s a huge loser polictically for Republicans.
Send Obama bills to veto, let to him whine, and find ways to submarine his executive orders. The people will turn against him even more as time goes on.
And pass a damn budget that cuts spending and abolishes some federal agencies, hah!! Dare HIM to shut the government down!
In other words be smart, not dumb!
The "will of the people" is whatever the press implants. Both parties in government see the government as the purveyor of fixes, and the people seem to at least accept this, if not demand it.