Watch: Rubio's brutal response to Trump on Cuba

Who knows if anything at a debate will ever hurt Donald Trump. But if anything should matter in the absolutely critical state of Florida, it's the above exchange with Marco Rubio at CNN's Thursday debate.

Anchor Jake Tapper was pressing Trump on whether he would continue Obama's outreach to Cuba. Trump's answer was vague nonsense: he talked about Cuba suing America somehow, and then said "I would want to make a good deal, a strong, solid, good deal."

Tapper forced the issue, asking Trump whether he would close the Cuban embassy or keep it open. Trump said that "I would probably have the embassy closed until a really good deal was made and struck by the United States."

And that's when Rubio pounced:

First of all, the embassy, the the former consulate, it's the same building. We can just go back to calling it the consulate. We don't have to close it that way.

Secondly I don't know where they're going to sue us. But if they sue us in a court in Miami, they're going to lose.

Third, on the issue of a good deal is: I know what a good deal is, it's already codified.

Here is a good deal. Cuba has free elections, Cuba stops putting people in jail for speaking out. Cuba has freedom of the press. Cuba kicks out the Russians from Lourdes, and kicks out the Chinese listening station at Bejucal. Cuba it stops helping North Korea invade [sic] U.N. Sanctions. Cuba takes all of those fugitives from American justice, including the cop killer from New Jersey and send her back to the United States, to jail where she belongs.

And you know what? Then we can have a good relationship with Cuba. That's a good deal.

Cue massive applause.

Politically, Rubio's answer was devastatingly good. His first two points highlight that Trump has literally no understanding of the details of Cuba policy — an issue that matters greatly to Florida's politically influential Cuban-American community. The last part of his answer is the kind of hard line on Cuba that's popular among Cuban-American conservatives, many of whom fled the revolution and haven't forgiven the Castro regime for their dispossession.

Substantively, Rubio's position — keep up the US embargo on commerce with and travel to Cuba until they democratize — is a proven failure. The US embargo has been in place for decades, in various forms, and has had no discernible effect on Cuba's human rights record. It is currently opposed by 97 percent of the world's countries as well as a majority of Americans. There are very good reasons why Barack Obama is working to end the embargo.

But Rubio's line is incredibly popular with a key Republican constituency in Florida: conservative Cuban-Americans like Rubio himself. Rubio understands the state he represents, and wielded that knowledge very effectively against Trump at Thursday's debate.

Whether that can close the gap between him and Trump in the Florida polls, however, remains to be seen.