Postgresql can handle unlimited amounts of data, limited only by your hardware for the most part. There are multi-terabyte databases running on it.
The maximum size for a text field is 2 gigs. Maximum number of rows is unlimited, maximum number of fields in a row is 1599.
More importantly than just being able to store a terabyte, is being able to do so in a reliable and speedy manner. No database server is gonna toss around 150 gigs at a time quickly. But a poorly designed one will have many more problems than a good one.
Are you talking about lots of small rows in disparate tables, or a few VERY large rows in a couple of tables?
Do you need lots of foreign key constraints, and are you going to do lots of fancy data extraction on it? Or a simple data store? Do you need Full Text Searching? Or are you gonna calculate the location on the globe of all the major cities?
Our knowing what exactly you're gonna do with your database makes a big difference here in helping to give ya pointers.