It would have been better if you had given an actual link to the article,
which is here for the record.
But anyway, that's your backup. Now let's compare what your source says to what you claimed:
Well, first, the part you did quote doesn't back you up, as it says nothing about Biden, Hillary, or "all Democratic leaders." But rather oddly, you don't quote the entire final paragraph. Here it is in full with the sentence you removed bolded:
"In a recent survey of all the Democratic candidates, The Washington Post asked whether there should be restrictions on abortion at any point during a healthy pregnancy. Six of the candidates, including Buttigieg, Warren and Sanders, said they support no restrictions.
Biden and Sen. Amy Klobuchar (D-Minn.) responded that abortion should be unrestricted until the point of fetal viability, usually considered to be between 24 and 28 weeks of pregnancy."
Is there any particular reason why, when offering a quote from this article, you omitted the last sentence of that paragraph, which directly contradicts your claim?
Maybe Biden changed his mind and became more extreme later, but it's hard for me to take the claim seriously when apparently the best source you can find for backup actually contradicts the claim.
I don't like Biden myself, mind you... but again, it's important to judge him by what he's actually said, and (so far) evidence has not been presented that he--or Hillary, or "all Democratic leaders"--favors no abortion regulation at all, and in fact the evidence presented has stated the opposite for Biden.