I think that after 8 years of Obama, voters are ready for a change (just like after 8 years of Bush). The only hope the Democrats have are: (a) a centrist candidate, or at least one that pretends to be, or (b) a really bad Republican candidate.
The last unabashedly liberal candidate to run for President was George McGovern. He got creamed, by Nixon. Every subsequent Democrat candidate tried to run as a centrist. They weren't, for the most part. But, they managed to pull the wool over voter's eyes.
Warren can't do that. Unlike Obama, who avoided taking positions on anything, Warren has loudly proclaimed her progressive credentials.
She would easily beat Bush or Christie.