Unit tests take a little time to write, sure. But look what you get for your investment:
(for the sake of this discussion I'll avoid subjective issues such as improved design)
1) Faster feedback cycle - if you're developing new code you can run a single test and check inputs/outputs very quickly. If you're testing by refreshing a page, or shudder, restarting your java server, you're going to have to wait far longer to find out if your code changes work as expected.
2) Reduced risk when making changes to the code base - the risk increases the closer you get to your data store as the amount of dependent code increases. The only way to reduce risk without unit tests in place is to not change any code i.e. you have to keep building on top (see the open/closed principle). This inevitably means that your code is going to introduce duplication as you can't refactor it out where appropriate. The other option of course is that you just risk it and hope to god that your manual QA testing will catch any problems before your users do.
It's also worth noting that the cost of adding unit tests isn't fixed, it's dependent on
a) experience
b) the tooling available for your language
From personal experience I find adding unit tests in ruby takes very little time. This means that benefit 1 in particular kicks in far sooner. Currently I feel it's faster for me to write a piece of code with a unit test than without.