It was argued that the Due Process clause in the 14th amendment protects rights not previously recorded - one of them being a right to privacy. The case was that forbidding abortion violates a women's right to privacy.Where in the Constitution do women have the right to MURDER their unborn children
This has ALWAYS been a very weak argument - even Ruth Bader Ginsburg said so - the most ardent proponent of abortion rights.
She stated frequently that it could be argued under the Equal Protection Clause of the same amendment that since women alone can become pregnant, making a law that restricts them along is a violation of their equal treatment under the law.
Dobbs pretty much wiped out the previous definition. As many people believe - as I do - there really can't BE a more fair and democratic approach to the issue than to let the voters decide in each state. This is counter to the modus operandi of the Democratic Party who typically believe, when an issue is something they believe in - what the voters CHOOSE be damned. Hence, they wish to restore a constitutionally protected right to an abortion.
They can DO that, with an amendment - which I do not believe will pass. They can also do that with a re-working of a right to an abortion under the equal protection clause. I don't know how that works, but those are the two ways I know of.