Republican Senators in Arizona and Georgia Have a Problem: The Base

“They don’t buy her as a bona fide very conservative Republican,” said Chuck Coughlin, a longtime Republican political consultant in Arizona.

The candidates’ struggles speak to how real divisions among Republicans have been obscured by Mr. Trump’s victory in 2016, and could erupt again should he lose in November.

Ms. McSally, in particular, faces pressure from a nativist faction that wants her to be more vocal on restricting immigration. The extreme wealth of Ms. Loeffler, who has a net worth in the hundreds of millions and is married to the chairman of the New York Stock Exchange, has become an issue in her race, particularly since she faced criticism for stock transactions that coincided with the early days of the coronavirus pandemic.

Allies of Ms. Loeffler point to recent polling that showed a closer race than initial surveys suggested. This week, the senator — who is also a co-owner of the W.N.B.A.’s Atlanta Dream — announced she opposed the league’s plan to allow players to wear warm-up jerseys reading “Black Lives Matter” and “Say Her Name,” a move some saw as an attempt to shore up her conservative credentials.

In a statement provided by a campaign spokesman, Ms. Loeffler said, “Georgians want a conservative outsider like me — not another career politician like Doug Collins who has sided with liberal democrats like Stacey Abrams to raise taxes, restrict 2nd Amendment rights, oppose term limits, and fund sanctuary cities.”

Several Republicans in Arizona and Georgia said in interviews that the problem is not with Ms. Loeffler’s or Ms. McSally’s messages, but whether the base is buying the candidates as authentic. . As a sign of their shared troubles among Republicans, some of the most negative publicity for both senators in the past year has come courtesy of Fox News, the cable outlet that is often sympathetic to the president.

Ms. McSally was pressed repeatedly by the conservative host Laura Ingraham during Mr. Trump’s impeachment trial about whether she wanted the Senate to call witnesses, and refused to answer. Ms. Loeffler has denied wrongdoing regarding the stock transactions, but when news broke one of her largest detractors was another host, Tucker Carlson.