Sallie Mae's talks with private equity on a $20 billion buyout could hit a snag due to "significant political headwinds" facing the largest U.S. student loan company, CNBC's David Faber reported.

Faber said the total size of the deal would be $30 billion, including $10 billion in debt. That confirms the New York Times' first report of a possible LBO of Sallie Mae that could top $20 billion, about a 20% premium on its stock price. Sources told Faber that Blackstone Group is a potential bidder. Neither Sallie Mae nor Blackstone would comment on the reports.