It emerged that Mr Hodgkinson, who died of his injuries following a gunfight with police, was a volunteer for Senator Bernie Sanders’ presidential campaign and promoted anti-Republican rhetoric on social media.
Mr Carver, the Republican Party chairman in Georgia’s 11th Congressional District, told the Post «the shooting is going to win this election for us».
He went on: «Moderates and independents in this district are tired of left-wing extremism. I get that there’s extremists on both sides, but we are not seeing them.»
The much-anticipated election in the Atlanta suburban district between Ms Handel and Mr Ossoff is seen as a test of President Donald Trump popularity.
The showdown is also considered the most expensive US House of Representatives race in the nation’s history.
Mr Carver praised Mr Ossoff for running a «brilliant campaign», but contended the baseball shooting would tip the outcome in Republican favour.
«We’re seeing absolute resistance to everything this president does,» he added.
«Moderates and independents out there want to give him a chance. Democrats have never given this president a chance.»
His comments came as a Republican group released an advertisement attempting to link the congressional shooting to Mr Ossoff’s Democratic campaign.
The television spot, produced by the Principled PAC, showed an image of Mr Scalise on a stretcher after the attack.
«The unhinged left is endorsing and applauding shooting Republicans,» a narrator is heard saying in the ad.
«When will it stop? It won’t if Jon Ossoff wins on Tuesday.»