I don't think they are in danger of becoming the next Williams.
They have a bigger budget and have a very good business/commercial team filling their coffers. They are also happy to "sell out" and advertise themselves heavily. This is something I never once saw Williams do. I'm assuming that if sponsors such as Vodaphone are allowed to use a team's car/drivers in their adverts, that the sponsorship deal for the year, will be higher.
I think Williams are very proud of their purist/F1 engineering team status. Ultimately, this meant that their budget never climbed at the same rate as McLaren and they fell behind the leaders.
Furthermore, in Willams' case, they lost Mansell, Prost, Senna, Hill, JV, in (almost) successive years. All of them world champs. You can't lose top class drivers at that rate and expect to still be competitive. They do not appear to have the ability to hold on to their World Champions. McLaren on the other hand do not suffer from this problem.
McLaren's big problem seems to be their design team. In the last few years, they have had a poor Winter, but are very good during the season. Another problem is that RBR have been stellar.