That the Republican Party has embraced someone willing to traffic in the most inflammatory of accusations comes as wish fulfillment for an element of the right that is convinced that the party lost the past two elections because its candidates were unwilling to attack President Obama forcefully enough.

In this telling, in 2008, Senator John McCain should have focused on Mr. Obama’s relationships with his former pastor, the Rev. Jeremiah Wright, and the onetime radical Bill Ayers, and on discredited claims about Mr. Obama’s birthplace and ties to Islam. And Mitt Romney lost four years later because he, too, ignored those issues, as well as other fixations of the conservative news media like the terrorist attack on the United States Consulate in Benghazi, Libya…

“He’s never been involved in policy making or party building or the normal things a candidate would do,” said Jon Seaton, a Republican strategist. “His whole frame of reference is daytime Fox News and Infowars,” a website run by the conservative commentator Alex Jones.

Mark Salter, Mr. McCain’s former chief of staff, said Mr. Trump was making common cause with “the lunatic fringe,” citing his willingness to appear on the radio show of Mr. Jones, who has claimed that Michelle Obama is a man.