In the 2012 presidential campaign, June was a pivotal month for President Obama’s re-election efforts. Mitt Romney had emerged from a slashing primary race close to broke, looking to get to the nominating convention so he could reset his candidacy and get an infusion of cash.

While there is little that is similar between the candidacies of Mr. Romney and Donald J. Trump, the result may end up being the same.

Mr. Romney was defined by a brutal series of television ads aired by both Priorities USA, the “super PAC” supporting Mr. Obama, and his campaign. Mr. Romney, in those renderings, was a heartless corporate raider who talked about liking to fire people who did not provide good services, and whose private equity firm feasted on the modest-wage jobs of hard-working people.

Mr. Romney never recovered. But he was still only a few ticks behind Mr. Obama in the polls in June 2012. In the last week of June that year, Mr. Obama was at 47 percent, with Mr. Romney at 44 percent, according to an NBC/Wall Street Journal survey.