Warren says she won't back bipartisan abortion rights bill

The big picture: The bill introduced on Monday is designed to "enact in federal law the essential holdings of Roe v. Wade and related cases," per a statement from its co-sponsors, Democratic Sens. Tim Kaine (Va.) and Kyrsten Sinema (Ariz.), and Republican Sens. Lisa Murkowski (Alaska) and Susan Collins (Maine).

What they're saying: Warren, a longtime abortion rights advocate, told NBC's "Meet The Press" the "Kaine-Collins bill does not codify Roe" so she intends to vote "no."

• The "problem here is this bill is not an obvious improvement over where we stand right now," Warren added.

Meanwhile, referring to the Dobbs v. Jackson Women's Health Organization decision that overturned Roe v. Wade, Kaine told NBC News on Monday night that the bipartisan legislation hadn't so far secured 60 votes, but he had "a feeling that the post-Dobbs reality of 10-years-olds being smuggled across state borders" could help the measure succeed.

• He pointed out that the bill was written before the Supreme Court's abortion ruling. "Our bill is a time machine and we take the law back to where it was the day before Dobbs," Kaine said. "And not everybody loved that law, but at least it had the virtue of women had been able to rely on it for 50 years."

Go deeper... Dashboard: The latest on Roe v. Wade and abortion