The use of language seen as coded racism prompted an extraordinary rebuke from Fox News after DeSantis appeared on the network Wednesday.
In an appearance on MSNBC's "Meet the Press Daily", Gillum told host Chuck Todd that the voters of Florida are "better than this". Gillum is the first African-American nominee for the governorship of Florida. Republicans plan to use an FBI investigation of Tallahassee's municipal government against Gillum, though he's not directly been named a subject.
Gillum was able to defeat former Democratic congresswoman Gwen Graham and former Miami Beach Mayor Philip Levine, two establishment Democrats with a big-spending campaign despite spending the least amount of money and having the least television presence.
Gillum, the liberal mayor of state capital Tallahasee, won a surprising victory in the Democratic primary for Florida governor, and has said he hopes to motivate younger progressives and minority voters who normally sit out non-presidential elections.
When asked about the term, Gillum felt like it was a calculated tactic.
"There is a difference in getting some of the Bernie Sanders people to vote for you in a primary and then going to the broader Florida electorate and trying to sell that message", DeSantis said.
DeSantis' comments brought a swift rebuke from Terrie Rizzo, chairwoman of the Florida Democratic Party, who said they were racially tinged.
In favorability ratings, 45 percent of those surveyed said they have a favorable opinion of Gillum, and 27 percent an unfavorable opinion. The state capital has had one of Florida's highest crime rates in recent years, although it's been going down.
He tweeted: "Such a fantastic win for Ron DeSantis and the people of the Great State of Florida".
This is a dishonest rendering of what DeSantis said.
The new approach - being taken by Gillum and also Abrams in Georgia and some Democrats in other states - eschews moderation and emphasizes advocacy of strongly progressive positions.
At the White House, Mr Trump told reporters he had not heard about Mr DeSantis's comments, and praised the Republican candidate as "extraordinary".