Theory popularized by: Sportswriters, mostly; players who speak in clichés.
The numbers (examining the 52 Super Bowl teams since 1978)
Overall winning percentage: 630-185-1 (.773)
Winning percentage, final week: 40-12 (.769)
Winning percentage, final two weeks: 83-21 (.798)
As a group, Super Bowl teams play just as well over the last week and two weeks as they do over the entire season (that difference in winning percentage between the final two weeks and overall is just two wins).
In other words, there is no such thing as needing momentum heading into the playoffs.
Theory applied to 2004 playoff teams
On the other hand (take note, Eagles fans), none of the 52 Super Bowl teams lost its final two games. (The 1996-97 Broncos, winners of back-to-back Super Bowls, lost two of their final three games both seasons.)
Which makes sense: you have to be very good to make the Super Bowl and very good teams don't lose two games in a row. That makes the Eagles a unique case, a 13-3 team which did lose its final two games. The Falcons, Vikings and Jets also lost their final two -- and look what the Jets and Vikings did in the first round.