At a news conference Thursday, Obama said his administration would provide a full accounting shortly but declined to elaborate. Rep. Joe Sestak had said earlier this year that he was offered a job if he abandoned his Senate bid. Republicans and some Democrats have called for an explanation from the White House.
Last week, Sestak defeated Specter, the White House-backed candidate in the primary.
Specter ditched the GOP last year and became a Democrat to avoid a tough Republican primary.