I've applied for dozens of local government jobs in Texas that I was qualified for and never got contacted by them. Could this possibly be due to my resume? I have a business resume but do I need to format it?
Generally no. You do not need a "special" resume when applying for a government job. Very likely that you were qualified but someone else was more qualified. I've applied to multiple jobs and never heard a peep, even though I formatted my resume individually for each job. However, there are lots of government jobs that have specific requirements, skills, etc. that you need to show on your resume - but that's no different than tailoring a resume for any other job.
You don't need a special resume, but you should always tailor your resume to the job you are applying for, no matter who the employer. There is no use in listing skills or experiences that have no bearing on the position. Show that you actually did your homework on the position and get your resume to highlight the things they are especially looking for.
Large employers, like government agencies, that have to sift through hundreds of resumes will often run them through a keyword search to weed them out. It is entirely possible that you are perfectly qualified for the job but your resume is getting thrown out by the computer because you didn't use the right words. But you can usually find the right keywords to include in the job posting. Again, tailor your resume to the job you are applying for.
(I have a sister who works in the Minnesota state government and has applied to many positions there. She told me that when she heard about the way they filter out resumes by computer and started fixing up her resume to include the words they were looking for, her rate of interview callbacks about doubled.)