The president will especially consider how potential nominees view the Supreme Court's recent, controversial decision in the "Citizens United" campaign finance reform case, Crawford told host Bob Schieffer.
Mr. Obama himself took an during his State of the Union address, saying the ruling would "open the floodgates" to special interest money in political campaigns.
On Friday, the president again referenced the case when , saying that he will choose a nominee "who, like Justice Stevens, knows that in a democracy, powerful interests must not be allowed to drown out the voices of ordinary citizens."
"That statement was calculated and deliberate," Crawford said. "They're going to have a nominee that they think can prove Democrats, not Republicans, understand everyday Americans."
Nevertheless, Crawford said, Mr. Obama is likely to avoid nominating anyone Republicans could potentially filibuster.
"They don't want that kind of fight," she said.
The president will have to balance his interest in nominating a progressive candidate with consideration for whom he could get confirmed.
The current top contenders, Crawford said, are believed to be Federal Appellate Judge Diane Wood, Solicitor General Elena Kagan, and Federal Judge Merrick Garland.
More Coverage of John Paul Stevens' Retirement:
Supreme Court Justice John Paul Stevens Retiring
Read Justice Stevens' letter to President Obama
Obama Praises John Paul Stevens, Seeks Nominee With Similar Qualities
Obama on Justice Stevens' Retirement
Kagan, Wood, Head List of Likely Court Nominees
Replacing John Paul Stevens: A Strategic, Not Political Pick