Mr. O’Rourke has also acknowledged, in both public and private settings, that the early stages of his presidential campaign gave the impression of excessive self-regard, starting with a romantic portrait on the cover of Vanity Fair that heralded his entry into the race.

In other ways, Mr. O’Rourke’s determination to proceed as a man unburdened by a traditional schedule of early-state rituals recalls the comparatively freewheeling and self-directed mode of campaigning he employed in his challenge to Senator Ted Cruz last year.

Over the last two weeks, Mr. O’Rourke has been a more resonant figure in the primary contest, speaking out from his wounded city in raw and emotional terms. And he has flashed glimpses of the traits that made him a hero to liberals in the midterm elections — his willingness to confront a right-wing adversary in plain language, for one, and his authentic passion on issues of immigration and national identity.

It remains to be seen whether Democrats are likely to find Mr. O’Rourke a similarly affecting spokesman on matters far outside El Paso and the immediate circumstances of the tragedy there. He has been facing a chorus of pleas, from Democrats in Texas and Washington, to leave the presidential race and run again for the Senate, challenging Senator John Cornyn, a senior Republican. The filing deadline for the race is not until December.

But Mr. O’Rourke has consistently rebuffed those entreaties, and in his speech he said a Senate campaign would not be “good enough” for this political moment. His campaign aides have grown frustrated with the pressure being applied to Mr. O’Rourke by fellow Democrats and the persistent, Senate-themed questions he receives from the news media.

An editorial in The Houston Chronicle this week urged him: “Beto, come home. Texas needs you.”

Mr. O’Rourke may still struggle to stand out in the presidential primary: He is far from the only Democratic candidate to blame Mr. Trump for creating a toxic and dangerous social atmosphere that has left Latinos and other minority groups vulnerable to violence. Nor is he the only candidate to design his campaign schedule around acts by Mr. Trump and other Republicans that Democrats find appalling.

Julián Castro, the former housing secretary and a fellow Texan, has been running ads on Fox News decrying the El Paso massacre that targeted people who “look like me.” In July, Mr. Booker, the New Jersey senator, crossed over the border with Mexico and returned with several migrants seeking asylum. And last week he delivered a searing speech on race at the Emanuel A.M.E. Church in Charleston, S.C., the site of another mass shooting by a white supremacist. In May, Senator Kirsten Gillibrand of New York campaigned in Atlanta after Georgia’s Republican-dominated government enacted strict new limits on abortion.