A Washington Post-ABC News poll in 2009 -- the last one that was conducted on the subject -- showed that two-thirds of Americans (66 percent) wanted to establish diplomatic relations with Cuba, while 27 percent opposed doing so.
And views on the matter have shifted rapidly -- about as rapidly as anything in politics, in fact. In 1998, Americans opposed setting up diplomatic relations, 56 percent to 38 percent. Since then, they have gradually and steadily embraced more open relations.
People are somewhat less keen on the idea of ending the trade embargo and opening travel to Cuba -- two other major issues at hand as the two countries engage in talks. But both still had majority support; 57 percent wanted to end the embargo, while 55 percent wanted to end travel restrictions.
(Since this poll was conducted, the Obama administration has eased some travel restrictions.)
This, of course, does not mean that the Obama administration's decision will be politically popular. As the immigration executive action showed, even if the policy is popular on its face, the action itself might not be. Once people have a chance to digest what has happened and debate the pros and cons, things can shift.
And some already are crying foul -- in particular about the move to exchange three jailed Cuban spies for an American one and the "humanitarian" release of American Alan Gross, who had been imprisoned in Cuba for five years. That exchange will be part of the conversation, and might be a tougher sell.
As you may have guessed, Republicans are the least receptive to opening things up with Cuba. The Washington Post-ABC News poll from 2009 showed them split on the question, with 47 percent supporting diplomatic relations and 46 percent opposing. So clearly, there will be some GOP opposition to this -- and there already has been.
This is the political backdrop against which the White House makes its announcement Wednesday.
Scott Clement contributed to this report.