The rollout of the Democrat's new position was "terrible staff work" and looked like "jackleg stumbling," Stirewalt said during an appearance Friday on "The Daily Briefing."
Biden disavowed his support for the Hyde Amendment, telling supporters, "Health care is a right. I can no longer support an amendment that makes that right dependent on someone's zip code."
The Hyde Amendment, named for former Rep. Henry Hyde, R-Ill., prohibits the use of federal funds for abortion procedures except in special cases like saving the life of the mother.
Stirewalt pointed to a report in The Atlantic magazine claiming Biden's campaign staff thought his position on the Hyde Amendment would be troublesome in the Democratic primary, and successfully convinced him to change his tune.
Milano spoke to Biden campaign manager Greg Schultz over the phone, urging him to have the former Delaware senator change his mind, according to the report.
"[His staff] were listening to Alyssa Milano," Stirewalt said. "They were getting pressure from her and pressure from others. Biden was resistant."
"So, his own staff rolled him and allowed external pressures to hurt him - and then let him come out with this sort of jackleg stumbling into making this reversal of a position that he's held for 40 years," Stirewalt added.
He called the situation, "terrible staff work."
Host Dana Perino added one of Biden's primary challengers, Rep. Seth Moulton, D-Mass., applauded him for "doing the right thing," but said he now should consider changing his position on the Iraq War.