Totally agree on that last part. The pain rapidly diminishes as you come up with simpler ways to do things in a reusable way. Also, the tools to do it are getting better and better as more and more people are feeling the same pain.
For instance, properly escaping output, parameterized queries, password hashing -- all those don't require more work (or if they do, it's so, so minimal). I mean, jeez, you're writing the code, just do it right.
That's a far cry from setting up multiple servers, certificates, etc. and having a real operations process. I can forgive, say, not having automatic builds. But there's no excuse for having a SQL injection in 2012.
Disclaiming though, I clearly state to such clients that security will not be really up to challenge on those timelines. They usually don't care, even to a point that I don't really bother anyone with it, since I get blank stares when I discuss security with them.
I can assure you that the blank stares go away completely when there is a breach. You will probably learn by then that your customers just expect you to handle it professionally. They might not be able to think beyond their deadline and their first business goal, but leaking passwords or losing user data will be your fault eventually.
I will not pretend that all my past work is bulletproof, but it should be not so difficult to make sure your tools and code handle all incoming data like hot grenades. You might skip some big-upfront-user-import in the beginning as you control the data chain, but $_POST or params[:model] or what else is flying in your face should be met with a standard treatment.
Think of it this way: right now you do not want to have your CV say "2012: developed user login module for LinkedIn. Finished within the deadline"
This adds a bit more up front planning pain to any project and also slightly slows down the daily dev routine BUT it pays dividends further down the line when you suddenly start getting noticed and your usage figures begin multiplying every 24 hours. In that situation there isn't time to re-work production dbms schemas, change the app code to deal with bcrypt'd password hashes, change the deployment script to make it more secure so you don't end up accidentally dropping a dev version of the site on your public servers etc. etc.
Better to pay the up front cost of getting the basics correct at the beginning of the project rather than dealing with an un-contained explosion later on just as you hit the limelight.
Also, the up-front pain of doing this diminishes with every additional project you do as a lot of the concepts, approaches and procedures are re-usable.