No, because it would obviously backfire. When the progressives did challenge a Democratic incumbent president for being too centre in 1980 the end result was Ronald Reagan. The two following Democratic presidents governed even further right but were not challenged and won their reelections.
Are you insane? Obama is on par with LBJ, perhaps left of him depending on how much weight you give to foreign policy.
Yeah Obama may not be a true leftist hero but he is way to the left of Clinton or Carter.
Bernie will be too old, and I don't see Warren doing it. The only person with enough stature to who might would be Fiengold but even that would surprise me unless Hillary starts a war or something.