Photo

As the Republican presidential primary has shifted into gridlock, the Democratic race has become something of a staring contest between allies of Hillary Clinton and Senator Bernie Sanders of Vermont.

Among those Clinton allies is President Obama, who, while he has praised Mr. Sanders and said he would be a good president, made clear at a private fund-raiser for the Democratic National Committee in Texas last Friday that he sees the arc of the senator’s candidacy drawing to a conclusion fairly soon. The party, he said, according to three people in the room, must come together. And while Mr. Obama acknowledged that Mrs. Clinton has perceived weaknesses as a candidate, and that some Democrats view her as inauthentic, he suggested, essentially, that authenticity is overrated in a president.

He pointed to his predecessor, President George W. Bush, as an example. A White House official confirmed Mr. Obama’s comments.

Those remarks were met with deep anger by supporters of Mr. Sanders, who voiced their displeasure on social media throughout the day. Mr. Sanders has vowed to fight on, pointing to coming voting in states with demographics that are likely to favor him over Mrs. Clinton.

If the de facto leader of the Democrats, however, is looking to start mending his party, the Republican circular firing squad is only expanding. Mr. Trump stayed uncharacteristically out of sight on Thursday, save for occasional tweets about his rivals or his critics.

But, as he has for almost a year, he dominated the conversation from Washington to New York. Those looking to stop Mr. Trump began airing ads in Arizona and Utah, states that will hold nominating contests on Tuesday. But even Representative Paul D. Ryan of Wisconsin, the Republican speaker of the House, conceded that a contested convention is looking like more of a reality.