Most teams don't like to play games several time zones removed from their home in consecutive weeks. It forces them to either deal with a lot of jet lag, or (more commonly) it forces them to stay away from home for two weeks in order to remain acclimated to the time difference.
Buffalo Bills head coach Rex Ryan is very much against the idea, and apparently felt so strongly about it that he specifically requested to avoid it this coming season, when the Bills will travel to Seattle, Oakland, and Los Angeles for road games. It seems that the NFL was inclined to grant his request:
This hasn't been a major issue in the past, unlike the reverse situation of Pacific-based teams playing consecutive road games on the east coast, but the move of the Rams from the Central to the Pacific time zone might make this more of an issue going forward.
Of course, there's also something to be said about the idea of making three separate trips across the country, which includes three separate trips back home. Constant time shifts aren't ideal, and if those three games are especially close to each other, it might do more harm than good.
The most recent instance of an east coast team playing two straight games in the Pacific time zone was in 2008, when New England was forced to do it on two separate occasions. They split the first instance, losing to San Diego after beating San Francisco, and later in the season swept Seattle and Arizona (which doesn't observe daylight savings time).
For their part, the Bills haven't played on the west coast in consecutive weeks since the end of the 1961 season. They dropped the finale to a San Diego team led by a young quarterback named Jack Kemp. Needless to say, it's been a while since the Bills have had to stay out there. They haven't even had to play two west coast games in the same season since 2004. Fortunately, there's a good chance that it should be a while before they have to worry about this again.