Newt Gingrich, for instance, was elected speaker after the Republican revolution in 1994. But by the midterm elections in 1998, when Republicans lost, rather than gained seats in the House as expected, Gingrich stepped aside, even though his party maintained majority control.
Strahan said there are two main functions of a House speaker: to usher legislation through Congress and to maintain a Congressional majority.
Pelosi, he said, has been wildly successful as a legislator. "She has passed one of the biggest most important pieces of social welfare legislation in history," he said, referring to the health care reform law.
"She's been very successful at advancing the party's legislative agenda in the House, but less successful at building and maintaining the majority, which is the other role of the Speaker," said Strahan.
ABC's Michelle Dubert contributed to this report.