If the qualifications are up to snuff, the chances of getting in aren’t bad. While the competition is fierce, the United States is currently producing fewer and fewer Engineers. The job market for Engineering is in an interesting state currently as there are more jobs than there are qualified applicants for.
However, the government does tend to be a little pickier when hiring than the private sector might be for the same position. Rather than accept subpar hires, the government is more likely to recruit from technology companies.
The best bet for getting in is to get hired by one of the companies that are subcontracted by the government to develop their technologies. These firms are more likely to hire someone with potential and develop them.