Hodgkinson was a 66-year-old man from Belleville, Illinois, according to the Associated Press.
In his speech, Sanders said real change "can only come about through nonviolent action, and anything else runs against our most deeply held American values".
"A gentleman walked up to us and wanted to know whether there were Republicans or Democrats practising out there", Mr DeSantis told CNN. He said he grabbed Scalise's phone to call his wife.
"Immediately, Jeff and I looked at each other and said, "We've got to report this individual".
Hodgkinson is suspected in a shooting that injured Rep. Steve Scalise and several others Wednesday morning. President Donald Trump said the gunman had been killed. Trump Has Destroyed Our Democracy.
Trump confirmed during a White House address that Hodgkinson died following injuries he incurred from a shootout with Capitol Police on the scene.
Five people were shot in Alexandria, Virginia Wednesday morning.
Hodgkinson, who worked as a building inspector, volunteered for the Mr Sanders' unsuccessful presidential campaign a year ago.
In a statement, Mr Sanders said he was "sickened by this despicable act". "He was a working man", said Matthew Jett, who works at the Main St. Cafe in Belleville, where Hodgkinson was a regular.
Texas Lt. Gov. Dan Patrick also released a statement on the shooting, saying hatred and violence have no place in society.
In April 2006, he was arrested on two counts of battery - one for striking a man in the face with a wood shotgun stock and another for punching a woman with his fist, as well as a count of unlawful damage to a motor vehicle for cutting the passenger seatbelt of the woman's auto with a knife. He told KCCI "Our computer records show that he volunteers for one debate watch party in Iowa. I am thankful that the shooter was apprehended by law enforcement quickly, and his deadly intentions were not fully realized", Patrick said.
Scalise is now undergoing surgery.
Trump said House Majority Whip Steve Scalise, two Capitol police officers, and at least two others were wounded in the shooting.
Moments after the attack, Trump said; "We may have our differences, but we do well in times like these to remember that everyone who serves in our nation's capital is here because, above all, they love our country".
"America is praying for you and America is praying for all of the victims of this awful shooting", the President said.
House Speaker Paul Ryan's office said Scalise's wounds were not believed to be life-threatening and that a member of the security detail was also shot.
But he was also "rough around the edges", according to an acquaintance, and local media reported he had a number of run-ins with local police, including for assaulting friends of his daughter in an 2006 incident.