Fact Check: Needs context

Walz has falsely claimed that Project 2025 will require pregnant women to register with a new federal agency designed to monitor their pregnancies. While the Project 2025 policy proposal is firmly against abortion, it does not call for monitoring pregnancies. It does, however, call for states to track abortions more meticulously than current CDC rules mandate, or else face punishment like cuts to federal funding.

Vance and Trump have also both said that Project 2025 is not associated with their campaign.

It’s worth noting, however, that Trump told Time Magazine in April that states could decide to start monitoring pregnancies as a way to track illegal abortions, saying that overturning Roe vs. Wade returned those decisions to the states.

“I think they might do that. Again, you'll have to speak to the individual states. Look, Roe v. Wade was all about bringing it back to the states,” he told Time.

More broadly on the subject of abortion, Project 2025 does call for an end to the FDA’s approval of mifepristone, a widely used abortion medication, and calls for a revival of a 150-year-old law that bans the shipment of abortion related equipment and medicine from being sent via the U.S. Postal Service, which would make it much more difficult for women who are taking the drug legally to access the care.

In August, Trump signaled he was open to revoking mifepristone access during a press conference in Mar-A-Lago, when he responded to a reporter's question about whether he would direct the FDA to ban the drug. “You could do things that … would supplement. Absolutely. And those things are pretty open and humane,” Trump said, while also emphasizing at that conference that he wanted to “give everybody a vote” on the issue.

When asked to clarify those remarks, Trump’s campaign pointed to the former President’s belief that abortion laws should be left to the states. The former President has also said he would not sign a federal abortion ban into law.

—Justin Fishel

Vance said a few times in this debate that Republicans need to "win back people's trust" on the issue of abortion, and the polls support that.

Abortion is important to many voters this cycle, especially women and Democrats. And they trust Harris more than Trump on the issue. In an ABC News/Washington Post/Ipsos poll from August, they gave Harris a 12 point lead on the issue over Trump.

Since the U.S. Supreme Court's decision overturning Roe v. Wade, more Americans have also expanded their view of abortion rights and don't want states to put limits on the procedure. KFF has found that nearly three-quarters of reproductive-age women oppose leaving abortion access up to the states, as Trump and Vance have said they support.

Democrats have been working in states across the country to paint Republican candidates as too extreme on the issue, and are hoping it drives voters to the polls as it has the past two years.

—538's Monica Potts

Fact Check: False

When running for Senate in 2022, Vance signaled support for a bill introduced by Republican Sen. Lindsey Graham that would ban abortion after 15 weeks nationwide. Vance called it "totally reasonable to say you cannot abort a baby, especially for elective reasons, after 15 weeks of gestation."

Also during his 2022 Senate race, Vance said he supported setting “some minimum national standard” in an interview with USA Today.

—Cheyenne Haslett

At times getting personal about home ownership, Walz defended Harris' plan to build three million new homes.

"I think we should be able to find some common ground," Walz said. "But we can't blame immigrants for the only reason that's not the case that's happening in many cities, the fact of the matter is, is that we don't have enough naturally affording affordable housing, but we can make sure that the government's there to help kick start it."

Vance continued to claim illegal immigration is responsible for higher prices.

"Tim just said something that I agree with. We don't want to blame immigrants for higher housing prices, but we do want to blame Kamala Harris for letting in millions of illegal aliens into this country, which does drive up cost," he said.

CBS News' moderators then asked Vance for evidence that illegal immigration is leading to higher home prices. He said there was a "Federal Reserve" study he said he would share after the debate but did not elaborate.