CINCINNATI — Hillary Clinton and Elizabeth Warren appeared together Monday in a cavernous hall before an army of adoring fans, amid rampant speculation that their joint swing-state rally was an audition for the Democratic ticket.

Each made vigorous arguments for the liberal policy points on which they agree, and the room turned electric — at times feeling almost like a Bernie Sanders rally — when the presumptive Democratic nominee and the Massachusetts senator zeroed in on Donald Trump.

But as the party increasingly consolidates around Clinton — and a new series of polls shows her nationwide lead expanding over Trump — the political logic behind the once widely held idea that Clinton needs the progressive icon on her ticket in order to win over skeptical Bernie Sanders voters is beginning to erode.

Clinton’s lead over Trump grew to 12 points this week, according to an ABC/Washington Post poll released Sunday; in the NBC/Wall Street Journal poll, it was 5 points.

Clinton’s favorability rating also climbed 15 points among Sanders supporters over the last month, according to the NBC/WSJ poll. Just as important, the number of Sanders supporters who say they’ll support Trump has dropped from 20 percent one month ago to 8 percent in June.

Together, the numbers are painting a picture of a presumptive nominee who will have more leeway in selecting her running mate than anyone expected just a month ago.

"The Sanders voters will come on board [because] the decision will be Clinton vs. Trump, not Clinton vs. Sanders," said Andrew Smith, director of the University of New Hampshire Survey Center, noting the rapid move of Sanders backers to Clinton already in her general election matchup against Trump. "I really don't think she needs to have them on board by having someone like Warren on the ticket."

"It's not like she needs [what Warren offers]," Smith added. "The Bernie voters are going to be on her side anyway in the general election, so trying to make calculations to assuage them doesn't make a ton of sense."

Either way, the presumptive nominee and liberal hero pounced on Monday at the opportunity to take a run at Trump in their first joint appearance since an October 2014 rally in Boston for gubernatorial candidate Martha Coakley — an appearance at which they didn’t actually stand on stage at the same time.

“Donald Trump says he’ll make America great again,” said Warren, who has relished her role as the party’s leading Trump antagonist in recent months. “It’s right there. It’s stamped on the front of his goofy hat. You want to see goofy?” she asked, invoking the nickname Trump has bestowed upon her. “Look at him in that hat."

While ripping Trump, Warren also found time to extol Clinton’s virtues.

“You know, I could do this all day, I really could. But I won’t, I won’t,” warned Warren, whose relationship with Clinton has never been particularly close even as they’ve kept in touch periodically over the course of the campaign, before the pair hugged to end the morning. “OK, one more. One more. Donald Trump calls African-Americans thugs, Muslims terrorists, Latinos rapists and criminals, and women bimbos. Hillary Clinton believes that racism, hatred, injustice and bigotry have no place in our country."

Speaking after Warren under a high ceiling and 1930s-era murals of workers, Clinton continued to let it rip, knocking Trump for celebrating Britain’s vote to leave the European Union as a potential boon for his Scottish golf course — while standing on that course.

“He tried to turn a global economic challenge into an infomercial. Imagine Donald Trump sitting in the Oval Office the next time America faces a crisis,” she exhorted the booing crowd. “We are not going to let Donald Trump bankrupt America the way he bankrupted his casinos. We need to write, we need to write a new chapter in the American dream, and it can’t be Chapter 11."

For all their apparent chemistry on the stump, the prospect of a Warren vice presidency is still in many ways a risky one, not least because of Warren's star power and her status as a lightning rod for many Republicans.

Shortly after Monday’s rally, for instance, Trump’s campaign pounced on the Massachusetts senator and her assumed role as a liberal-whisperer.

“As Clinton tries to salvage support among the Bernie Sanders wing of the Democrat Party, Senator Elizabeth Warren has become a turncoat for the causes she supposedly supports,” said a release from his team.

The Republican National Committee’s research team jumped in as well with a memo highlighting the distance between them on a series of policy points.

“We hope Bernie’s fans enjoyed Elizabeth Warren on the trail with Hillary Clinton just now, because they’re unlikely to see her join the ticket. The liberal icon exposes all that the left despises in Clinton: close ties to Wall Street, shifting positions on economic issues like trade and Social Security, and a dependence on the very big money special interests that Sanders and Warren rail against,” read the note. “A Clinton-Warren ticket is a nightmare for Brooklyn, forcing Hillary sharply left and giving a figure who outshines Hillary’s lackluster performance a bigger megaphone to promote her own activist agenda, which is at odds with Clinton’s."

But the argument against Warren’s inclusion may end up being superfluous as long as the polls suggest Clinton has a comfortable advantage and Sanders backers are coming home.

“There is no evidence that suggests that vice presidents can bring a significant bump to the president. They can help at the margins with a small or specific constituency group, or in their home state, perhaps by a couple of points, but no more than that. I don’t think we’ve seen a real significant vice presidential pick since Lyndon Johnson,” explained Monmouth University pollster Patrick Murray, whose school’s new poll shows no vice presidential contender swinging a significant number of voters toward Clinton, other than Sanders — who is not being considered.

“What I think is going to bring Sanders voters enthusiastically over to Hillary Clinton is if Bernie Sanders gives her a full-throated endorsement, and at that point the vice presidential pick doesn’t matter. Without that, Elizabeth Warren is not going to be much of a draw for them, because the cult of personality right now surrounding Sanders won’t go away."

And since — as people close to Clinton’s operation are quick to note — the most vehement anti-Clinton Sanders backers are clustered in liberal enclaves, not swing state locales like Cleveland or Tampa, they think the fear of a tough unification process is overblown.

“Trump is going to energize the liberal wing of the party; he’s the unwitting unifier of the Democratic Party,” said Bob Shrum, a senior adviser to the presidential campaigns of Al Gore and John Kerry.

But, he cautioned, “There’s no question that [Warren and] Hillary are very powerful together. She is also as good as anybody is ever going to be at protecting Clinton from Trump."

“You can go through all the conventional reasons” that she shouldn’t be picked, between the unprecedented nature of having a two-woman ticket, to her coming from a solid blue state, cautioned Shrum. But “they all sound like the reasons [Al] Gore shouldn’t have been picked."