Blumenthal reviews polling on it. Two important points:

First, while support for stricter gun laws has declined in the polls across several measures, Americans remain roughly evenly divided on the issue. The Pew Research Center found about equal numbers of Americans preferring to protect "the right to own guns" (46 percent) and to "control gun ownership" (47 percent). A modest increase in the second category would be enough to create majority support for stricter gun laws.

Second, there is broader support among Americans for incremental changes to gun laws. Polls by CNN and YouGov earlier this year found overwhelming support for several specific gun control policies: background checks, bans on gun sales to those with mental health problems, waiting periods before gun purchases and a national registry of gun ownership.

Harry Enten's advice to gun control advocates:

More then three in four, or 76%, of Americans want laws "requiring gun owners to register their guns with the local government". And 60% of Americans are against "high-capacity or extended ammunition clips". Gun control advocates would be wise to push proposals that implement these two gun control policies. They have majority support that can only grow after Newtown. It would be more difficult for Republican senators to oppose them – as they did with a bill to ban high-capacity clips this past July, when Democratic senators introduced legislation.

Nate Cohn believes that gun control could be a winning issue for Democrats: