Every time a job is posted on the UTA joblist or a tracking board, hundreds of resumes start to pour in. So there's no room for dillydallying when it comes to submitting your resume -- it’s really important to apply as soon as you possibly can, definitely within the same day of the posting. A lot of employers will cap the number of resumes they’ll accept, so the faster yours gets in, the better.
But take heed and don't rush your cover letter with something generic. Take the time to write a brand new cover letter, and do a once-over of your resume to make sure it's tailored to the job posting. This is one of the few times that you're at an advantage if you're unemployed -- you can shift your gears for the day and apply immediately. But if you do have a job, and your boss isn’t aware that you are looking to work elsewhere, don’t apply while you should be working. Use your lunch break or wait until you’re done with work for the day, whichever is first. It’s respectful to your current boss, and this will go a long way should the new job call for references.