Day said on Monday that "I just wanted to know if he [Buttigieg] thought there was room for us in the party. And he doesn't."
She told CNA that pro-life Democrats have been asking his campaign staff since December for a meeting, but no meeting has been offered. Instead, she decided to ask him in person at the townhall.
Buttigieg's comments came two months after Democratic presidential candidate Sen. Elizabeth Warren (D-Mass.) was asked at a Nov. 20 debate if there is room in the Democratic Party for a pro-life politician.
Warren said the party is "fundamentally" about preserving abortion access and that "abortion rights are human rights," but added that "I'm not here to try to drive anyone out of this party."
Day followed up her first question on Sunday evening by asking if Buttigieg if he would at least support language in the Democratic National Committee platform for 2020 that would recognize "diversity of views" on abortion within the party.
"Would you be open to language like that in the Democratic platform that really did say that our party is diverse, and inclusive, and we want everybody?" she asked the candidate on Sunday.
Buttigieg declined to support that language, instead calling abortion "medical care" that should be universally available.
"I support the position of my party, that this kind of medical care [abortion] needs to be available to everyone," he said.
While he said earlier Sunday evening that abortion should be left up to women, Buttigieg eventually said he did back limits on late-term abortions in line with the Supreme Court's 1973 Roe decision.
"I support the Roe v. Wade framework that holds that early in pregnancy there are very few restrictions, and late in pregnancy there are very few exceptions," he said.
He expressed his hope that pro-life Democrats will be willing to support him despite their disagreement on abortion.
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"And again, the best I can offer is that we may disagree on that very important issue, and hopefully, we will be able to partner on other issues," he said.
"I cannot imagine that a decision that a woman confronts is going to ever be better, medically or morally, because it's being dictated by any government official," Buttigieg said.
The president of the National Abortion Rights Action League, Ilyse Hogue, tweeted on Sunday evening that Day's question and the applause Buttigieg received for his answer "is a good reminder to differentiate between people who feel personally pro-life and those who are anti-choice like Kristen Day."
"The latter category believes it's fine to force their beliefs on others through law. The former does not," Hogue said.
Day told CNA that despite the applause for Buttigieg's answer, people sitting around her at the event supported her question to him and expressed disappointment in his response.
A 2019 CNN poll of likely Iowa Democratic Caucus attendees showed around 80% of respondents saying that a candidate's support for a "woman's right to abortion" was a "must-have."