Cuomo has no shot and as far as I'm concerned he'd get crushed in the general. A lot of progressives would stay home or vote third party and he's a gun grabber that has zero crossover appeal accept to moderate pro business types who live in blue states anyway.
Progressives voting third party en masse? Are you serious? First off, they'd likely view Walker, Bush, etc. as worse than Cuomo and vote for Cuomo to vote against the republican nominee. Second, let's look at some third party candidates in detail:
Johnson (Lib) - Complete Fiscal Conservative, Favors Legalizing Cocaine, Heroin, etc.
Stein (Gre) - Favors Legalizing Cocaine, Heroin, etc.
Anderson (Justice) - Complete Joke, couldn't even crack .1% in 2012.
Barr (Peace and Freedom) - See Anderson
-Constitution Party Candidate- LOLOLOLOL
None of the above would ever attract a large portion of today's progressive voters.