This week Ferrari and Renault threatened to pull out of F1 if the FIA went ahead with their proposed budget cap - see here and here. The budget cap, according to Ferrari, will create a two-tier system in F1. Teams that adopt the budget cap will have greater freedoms in car design, while teams that choose to spend more will have more restrictions.
The point is none of the teams will pull out and the FIA will not get a £40m budget cap, because of the totally stupid system of politics that operates in F1. Max Mosley and the FIA don't really want a £40m budget (at least not straight away), however the teams in F1 will not agree on anything unless the rule change is very radical. This leads to frankly ridiculous suggestions from which the teams can then negotiate down (and it also explains why F1 rule changes are so regularly in the news).
The teams (the FOTA) meanwhile see their participation in the sport as their only bargaining chip, and as so threaten to pull out if the rules aren't changed. However they never will, especially Ferrari. Many people have been asking whether F1 can survive without Ferrari, but real question is whether Ferrari can survive without F1. They are the only car manufacturer that can properly exploit a championship win - as they produce fast cars winning the championship is a real PR boost (Renault however do not produce fast cars and are more likely to pull out).
Basically both the FIA and the FOTA do not mean what they say, this however is not how the media see it. They take both of them at face value, meaning that the public often think that F1 is constantly bickering. I just wish that F1 would realise this and bicker about the rules behind closed doors (like every other sport).