Jared Bernstein, senior fellow at the Center on Budget and Policy Priorities, told "Squawk on the Street" on Monday that he isn't sure that Pence is the best running mate choice for Trump.
"One of the problems you have there is that he is very hard right on social issues, so those people are either already with Trump or they're a relatively small part of the base. He's completely different from Trump on so many key issues including trade, immigration, the Muslim ban, the wall," Bernstein said, adding that Pence could be "messing up his brand."
Sara Fagen, former White House director of political affairs for George W. Bush, disagreed and said that she thinks Pence "brings a lot to the ticket." In particular, she emphasized that social conservatives have not necessarily been behind Trump, contrary to Bernstein's analysis.
"The selection of Mike Pence is very helpful in that regard. It will help unify the base and give people who are concerned about Donald Trump, they will look at him differently and probably support him, whereas beforehand they were still up in the air," Fagen, who is also a CNBC contributor, said on "Squawk on the Street."
David McIntosh, a former congressman from Indiana, told "Squawk Alley" on Monday that he agreed with Fagen. He explained that Trump appeared to be a "liberal most of his life" and that picking Pence as his running mate, who McIntosh described as a "strong conservative," did in fact help the New York businessman unify the party.
Fagen acknowledged that Trump could have chosen a better running mate, especially if he had selected "somebody that could go directly against Donald Trump's weakness with women, with minorities," which Fagen argued "probably would have been a better longer-term play."