On March 1st there was such a poll published by YouGov (conducted at the end of February):
In a series of head to head questions we asked Britons whether their preferred Brexit choice would be to accept the draft Brexit deal, leave the EU without a deal or have a new referendum.
Taking the deal clearly beats leaving without any deal by 60% to 40%, while having another referendum leads the no deal option by a more modest 54% to 46%.
However, when asked to choose between accepting Theresa May’s draft deal and having another referendum, the public remain split down the middle. 51% would seek a new referendum in this scenario, while 49% would take the Brexit deal.
I'm leaving the rest of my answer below as has some fairly relevant info as well.
To unsatisfactorily answer my own question, a day before the no-deal survey, a third YouGov survey (March 12) found that the public was more evenly split on the November deal, 36% in favor to 32% against it. So no-deal and the November deal have nearly the same popularity (33% vs 36%), but no-deal elicits more opposition (46%) than the November deal (32%). That doesn't directly answer what the public would choose if they given only these two choices (no-deal vs November deal)...
I also found an older 3-way 2-choice survey (no-deal, November deal, no-Brexit) by Survation from November 28:
with the following interpretation:
For our respondent’s first preferences, the government’s Brexit deal is, as with the head to head style questions, less popular than leaving without a deal and clearly less popular than simply remaining in the EU. But critically, if asked to compromise – indicating their second preference, the PM’s deal becomes the least unpopular solution.
So if this one is to be believed, the government's deal would beat no-deal in a two-choice poll.
YouGov has conducted a similar 3-way poll in December. Their interpretation:
The results show that as things stand, when it comes to their first choices Theresa May’s deal is ahead in just two constituencies – the Tory-held constituencies of Broxbourne and Christchurch, and gaining just 27% across Britain.
That puts it behind Remain – which has 46% support nationally and is first preference in 600 constituencies – and level pegging with No Deal (also 27%), although No Deal is first choice in 30 seats. This model excludes the 12% of people who said they don’t know.
However, whist May’s deal is supported by just over a quarter of the public, the simple fact is that there is no majority support for any of the three options we presented, meaning that in order to find what outcome would gain majority support we should also look beyond the public’s first preferences.
And when the battle is turned from a three way split, where no compromise is needed, into straight two-way fights, Theresa May’s deal starts performing a lot better.
One way of analysing this is to use the “Condorcet method”. With this approach, instead of looking for which option is most people’s first choice, we should instead test which one beats all the others in a head-to-head fight. We do this by removing each option in turn, and then looking at the second choice of people who backed that option.
When we remove the Deal as an option and reallocate these preferences in a straight Remain Vs No Deal contest we find that Remain would be slightly ahead, winning 52% to 48%.
If the Deal is pitted against No Deal, the majority of Remainers swing behind what Theresa May is proposing, meaning it wins 65% to 35%. The calculation for Remain vs the Deal is a lot tighter. Although the vast majority of no dealers swing behind May’s plan, because Remain begins from a much higher starting point the result is a statistical dead heat – with 50% for each option.
