How to access Twitter REST API v1.1 using curl?
When you change the parameters, the OAuth signature base string does change, so the oauth_signature header does also change. That's why you can't reuse the signature when you change the parameters.
If you want to see the curl request for any specific request to Twitter API, have a look at the STTwitter library for OS X. The demo project includes a GUI client that will show you the OAuth request in curl format.
Now if your goal is just issuing requests to Twitter from command line, check out twurl which is a command-line client for Twitter API.