The New York Times ran a poll this month where they asked a question about whether people favored a "national health care plan in which all Americans get their insurance from a single government plan" or "government-run insurance to anyone who wants it, but people should be able to keep their private insurance if they prefer it" or reform health insurance without a government plan or no reform. The Times story on the poll chose to emphasize the fact that, even among Democrats, the single-payer/no private insurance was not the most popular choice, losing 58-25 to the public option choice.
But the rest of the results are interesting too. Just a fifth of independents favored single-payer, with twice as many favoring the public option. Between these two choices, you're approaching two-thirds of independents who would support a public option (assuming, which seems reasonable, that anyone who supported single-payer would also support a public option as an advance over the current system). And among Republicans, combining the two choices gets you to around one-third of Republicans.
So single-payer is a niche issue, polling poorly across the political spectrum, while a public option would get overwhelming support among Democrats, very strong support among independents and even pick up some respectable minority support among Republicans.
This does not seem like a difficult choice for the Democrats....if they want to win.