People To Contact
Hamilton Alum with Congressional Backgrounds (LinkedIn can help you find them)
Hamilton Washington Semester Professors
Congressional Committees (Pick a few whose jurisdiction interests you and then cold call them to inquire about internships)
Your Members of Congress (Whether it's the House or Senate, Members are always looking for applicants from their district or state)
One Last Tip
Feel free to shoot me an email at firstname.lastname@example.org and I'd be more than happy to let you know when I hear of openings from friends and former colleagues.