Are Americans uneasy with existing abortion laws welcome in the Democratic Party? That was the question put to several top Democratic leaders this weekend, prompted by a rally hosted by former presidential candidate Senator Bernie Sanders of Vermont for a Nebraska Democrat running for mayor of Omaha.

Last week, Mr. Sanders and Keith Ellison, a Minnesota congress member and deputy chairman of the Democratic National Committee, campaigned for Heath Mello, a Democrat trying to unseat the Republican mayor of Omaha. Some pro-choice leaders took issue with the endorsement, citing Mr. Mello’s past support for legislation advocated by some in the pro-life community, in this instance a modest proposal that doctors inform women considering an abortion about the opportunity to have an ultrasound scan.

On Sunday, Mr. Sanders doubled down on his endorsement and called for more openness in the Democratic Party.

Speaking on Face the Nation, Mr. Sanders highlighted his own “100 percent lifetime pro-choice voting record” but said that if Democrats are to be competitive in all 50 states, they have to welcome those who do not necessarily share those views.

“Well, I think what is clear to anyone who looks at where the Democratic Party today is, that the model of the Democratic Party is failing,” Mr. Sanders said.

“Clearly, the Democratic Party has got to change. And, in my view, what it has got to become is a grassroots party, a party which makes decisions from the bottom on up, a party which is more dependent on small donations than large donations,” he continued.

Following Mr. Sanders’s campaign event for Mr. Mello, Ilyse Hogue, the head of NARAL Pro-Choice America, said in a statement that the event was “not only disappointing, it is politically stupid.”

Senator Sanders: “I think what is clear to anyone who looks at where the Democratic Party today is that the model of the Democratic Party is failing.”

That prompted Tom Perez, head of the D.N.C., to issue two statements. In one, issued last Thursday, he seemed to defend Mr. Sanders’s decision to campaign for Mr. Mello—while reiterating the party’s support for abortion rights.

“Our job at the DNC is to help Democrats who have garnered support from voters in their community cross the finish line and win—from school board to Senate,” Mr. Perez said on April 20. “The biggest threat to women’s reproductive rights is the relentless Republican attacks on women’s health care, including legal, accessible abortion services. And I won’t let anyone get in the way of our fight to protect a woman’s right to choose.”

But in a statement issued Friday, Mr. Perez seemed to cast doubt on the big-tent approach, at least when it comes to abortion politics.

“Every Democrat, like every American, should support a woman’s right to make her own choices about her body and her health,” Mr. Perez said in a statement, according to The Huffington Post. “That is not negotiable and should not change city by city or state by state.”

“At a time when women’s rights are under assault from the White House, the Republican Congress, and in states across the country, we must speak up for this principle as loudly as ever and with one voice,” he continued.

(Though Mr. Sanders and Mr. Perez are traveling together to re-energize Democrats, Mr. Perez did not attend the Omaha rally.)

On Sunday, Mr. Sanders said he does not regret campaigning for Heath Mello, the Democrat running to unseat Omaha’s Republican mayor.

“It was a great rally, and I hope very much he wins,” Mr. Sanders said.

According to recent surveys, “our party is actually less popular than Trump,” she added. “That’s really hard to do.”

“Frustrating” is how Kristen Day, the executive director of Democrats For Life of America, describes a weekend spent following the news emerging out of Omaha and considering the increasingly precarious place of pro-life Democrats within the party.

It appears that the party’s new chairperson, she said, wishes to “bend everyone’s arm to NARAL’s position”—an outcome she believes would be a disaster for Democrats during the midterm elections and beyond. “I don’t think it’s ever been clearer: Change your position or get out.

“I really think this is a great gift for the Republicans,” Ms. Day said. “We could be talking about economic security for families or health care,” she said, “and uniting Democrats around those issues rather than saying this is the one non-negotiable issue.

“We should be looking for ways to grow the party, not weaken it; this makes me wonder if [Mr. Perez] is the right person to lead the party.”

The debate about pro-life Democrats has drawn in other Democratic leaders, who appeared on cable news shows eager to criticize President Donald Trump’s proposed budget, which calls for tax cuts for the wealthiest Americans and funding for a new border wall.

Senator Chuck Schumer of New York, the Senate minority leader, was pressed about the issue on Morning Joe on Monday.

“Look, we’re a big-tent party as Nancy Pelosi said, but let’s make no mistake about it, we’re a pro-choice party. We’re a strongly pro-choice party. We think that’s where the American people are, and, in fact, if anything, are moving even more in that direction,” Mr. Schumer said.

“But, you welcome pro-life Catholics?” host Joe Scarborough asked.

“I gave you my answer,” Mr. Schumer replied.

A 2016 poll from the Pew Research Center found that most Americans, 56 percent, said abortion should be legal in all or most cases. But there were sharp differences among Democrats and Republicans when it comes to abortion laws. While most Democrats say abortion should be legal, 28 percent said it should be illegal in all or most cases.

Over the weekend, when asked on Meet the Press if pro-life Americans could support the Democratic Party, House Minority Leader Nancy Pelosi said, “Of course.”

“I have served many years in Congress with members who have not shared my very positive, my family would say aggressive, position on promoting a woman’s right to choose,” Ms. Pelosi said.

And Senator Dick Durbin of Illinois, the Senate’s second-highest ranking Democrat, said on Sunday that the Democratic Party stands by its firm commitment to abortion rights but allowed that those who disagree are still welcome.

“I know within the ranks of the Democratic Party there are those who see that differently on a personal basis, but when it comes to the policy position I think we need to be clear and unequivocal,” Mr. Durbin said on CNN.

“We need to be understanding of those who take a different position because of personal conscience, but as long as they are prepared to back the law of Roe v. Wade, prepared to back women’s rights as we’ve defined them under the law, then I think they can be part of the [Democratic] Party,” he continued.

Ms. Day might argue that Democrats need to be a little more than just “understanding” of the pro-life position. With the number of elected Democrats in Congress and in statehouses across the country at the lowest level since the 1930s, “we are in a very serious position as a party,” Ms. Day said. According to recent surveys, “our party is actually less popular than Trump,” she added. “That’s really hard to do.”

The party cannot push through its legislative positions in the minority, and it cannot emerge from its minority status without the support of pro-life Democrats, she argues.

“We’re our own worst enemy right now,” she said. “We have not taken a close look at what’s wrong; we’re just grasping at straws [regarding the loss to Mr. Trump], ‘It’s the Russians,’ or ‘It’s the media and the emails.’

“The reality is that we are losing touch with our base,” she said. “We lost the ‘blue wall’ [of Pennsylvania, Wisconsin and Michigan]; that should have been a huge wake-up call.”

Now “we’re not really looking in the mirror at all and maybe listening to the wrong people…. We have California and New York—if that is all you want, keep doing what you’re doing, but we’re not going to win back Middle America with West Coast values.”

In Nebraska and in other upcoming elections, Ms. Day argues it would be an epic tactical error for Democrats to continue to use pro-choice positions as a litmus test for candidates.

About the only positive thing she can say about the internecine discord emerging out of Omaha is “this is an important conversation for the party to have.”

She believes the message of pro-life Democrats is worth hearing within the party and throughout the country. “We want women to have true choice,” she said. “We need to do a better job about providing support and options to women” so no one is economically cornered into a “choice” to have an abortion. That is an outcome she believes Democrats, with the support of their pro-life members, would be best positioned to achieve.

Kevin Clarke is America’s chief correspondent and the author of Oscar Romero: Love Must Win Out (Liturgical Press).