The Republican Party’s best hope to help candidates navigate this treacherous new territory could come from an unlikely source: Gov. Rick Scott, who is expected to announce on Monday that he is running for the United States Senate against Bill Nelson, the Democratic incumbent.

Mr. Scott, a multimillionaire former health care executive whose style is more suited to the boardroom than the stump, is not frequently sought to campaign for fellow Republicans. But if the governor operates as he has in the past, he will likely spend big and early on television ads that could benefit other Republicans unable to purchase much airtime in Florida’s expensive broadcast markets. His campaign team, unencumbered by a serious primary challenge, will be able to focus on mobilizing voters for the November general election.

In Mr. Scott, Mr. Nelson will face his toughest opponent since his election to the Senate in 2000; Democrats are expected to invest tens of millions of dollars to defend his seat. But Mr. Scott, too, will have to answer for Mr. Trump. He led a “super PAC” raising money for the president during the 2016 election, and has been a frequent guest at the White House and Mar-a-Lago, the president’s Palm Beach estate.

In the past year, as he has prepared for the Senate race, Mr. Scott has broken with the president several times. He pressed the White House to let 32,500 Haitians, living in Florida under temporary protected status, remain in the country. He opposed the end of the Deferred Action for Childhood Arrivals program that has protected many immigrants brought into the country illegally as children from deportation. He pushed against allowing oil drilling off Florida’s shores. And he made repeated trips to Puerto Rico in the aftermath of Hurricane Maria, trying to establish a response to the catastrophic storm that was more proactive than the federal government’s.

Most important, perhaps, Mr. Scott signed off on new restrictions on firearm purchases after the Parkland shooting in defiance of the National Rifle Association, neutralizing some of the opposition he would have otherwise faced from vocal students and their families. That has not stopped Democrats from accusing the governor of acting only when it was politically convenient, especially given the lack of state action after a gunman killed 49 people at the Pulse nightclub in Orlando in 2016.