Strategies for localizing large amounts of text in .NET applications
If you decide to go DB, check out this article: Creating a Data Driven ASP.NET LocalizationResource Provider and Editor by Rick Strahl and then download it for free
If you decide to still using resx, you can use Zeta Resource Editor to mitigate the pain.
I honestly don't know about the limitations of the resx files but, if there are some, you can do the following:
Create a table into the database which contains the translated texts. Then you would have to cache the loaded translated text when the website would be accessed.
Such approach would also help with the translation team, which doesn't have access to Visual Studio. The only problem I visualize is the creation of an extra WebApp which would allow the translation team to translate the texts. But still, it would be something simple.
In case you can't use the database for that, some XML files could do the job for you.
EDIT: I just found another alternative but using .txt files. That can also help you.
If there is so much content it looks more like a problem that should be attacked/would be solved by a Content Management System.