Firefox doesn't use your system keychain to store usernames and passwords, but Safari does. Turning off usernames and password in the AutoFill Tab of Safari's Preferences should keep it from accessing your keychain for information. But if you are continually being prompted for your login password, it's a sign that your login keychain is not working correctly.
The login keychain should be automatically unlocked when you successfully log into your user account. If repairing the keychain fails, you can remove the keychain, but keep in mind deleting a keychain is permanent and you will loose all the stored information in that keychain, including, but not limited to, usernames and passwords, secure notes and certificates. Here's how to permanently remove and recreate the keychain.
To Remove the login keychain
1) Open Keychain Access in /Applications/Utilities
2) Select the login Keychain from the list of keychains on the left side
3) Delete the login Keychain (File -> Delete Keychain "login")
4) When prompted Delete Files & References to the Login keychain.
To Recreate the login keychain
1) From the File menu, choose new keychain
2) Name the keychain "login" and save it in ~/Library/Keychains
3) For the keychain password, enter the same password that you use to log into your user account*
4) Verify the password and click "OK"
* If you enter a different password here, you will continuously be prompted to enter the password for the keychain "login".