What would your reasonable ideal job be with a public affairs degree? The possibilities are pretty wide-ranging. If we pretend that right out the gate you might get a chance to do something that actually approximates what you would want to do, knowing what it is might help in suggesting a path for you.
I never hire entry-level employees from headhunters. Most charge not only a "finder's fee" for the referral, but they also charge a percentage of your salary for some initial period of time, like the first year. It may sound good to you because the recruiter charges the employer rather than you, the employee, but you still get a raw deal. Let's say you were going to get a job for $50,000 and the recruiter will get 10% for the first year. That means I am paying $55,000 for an employee who may or may not pan out. If I am going to pay $55,000, I would rather give it all to the employee and hopefully get a theoretically "better" prospect than one I could get for $50,000. IMO, headhunters at entry-level are basically leeches. It is different for high-level hires. Sometimes a high-ranker somewhere will become available, but will only look for jobs discreetly through a headhunter and if you want to hire that type of person the only way to do it is to use a headhunter. A currently sitting CEO or head of a government agency is not going to go job hunting through Craigslist, for example.