To get a job as a game programmer, all you need is a Computer Science degree and a resume. Creating a mod or an independent game can be helpful towards making your resume stand out, but it is definitely not necessary. You can work on projects such as those while you start looking for full-time work, but you should start looking now, rather than putting it off in favor of mod/indie projects.
One of the best places to look through job postings is Gamasutra.com (it requires registration, but you should be registered if you want to be in the game industry, anyway). Another way is to look at the Jobs/Employment/Careers section of the webpages of game studios in your area, and in areas you would be ok moving to. Check out the webpages for your favorite developers as well. Some game studios will pay relocation for an entry-level programmer, others will not, so close to home is your best bet. There is a map here: http://gamedevmap.com/
that lists every game studio by city, with links to the webpage of each studio.
Apply for any job for which you meet at least 90?f the stated Requirements. If a job requires a shipped title, don't apply unless you fit every other requirement to a T (and even then it will be a very long shot). Pay close attention to the requirements, and to how the company wants you to send in your resume, cover letter, and code samples. Failing to follow instructions on resume submittal is one of the best ways to get your resume thrown in the trash.
If you have trouble finding a job as a programmer, you might want to look into Quality Assurance positions. These typically require no experience or particular education, but will let you get your foot in the door. Once you work at the company, you will hear about job positions that are never posted publicly, and you will get to work directly with the programming team, which will increase your chances of being able to move onto the team eventually.