Early Deadline Internships
While most internships have deadlines that are six weeks before the start of the internship period, there are a few that are six months before the start of the internship period. These include the State Department, the White House, and any internship offered within the Intelligence Community (think FBI, CIA, and NGA). These types of internships generally have application deadlines between October and December for the summer because these internships require security clearance.
National and political newspapers, such as the Washington Post, the New York Times, and the Economist, may also have early internship dates. These types of internships can be very valuable to those interested in journalism and political journalism. Many of those in high positions at the Washington Post started out as interns. Also, interns regularly have their own stories published, allowing them to gain exposure and build their portfolio of writing samples.
Here is a short list of the organizations listed above:
It is definitely a great idea to start your search early and compile an Excel database that lists deadlines, material requested (cover letter, letters of recommendation, resume, etc), and any other relevant information. Further, in requesting letters of recommendations from teachers, employers, or advisers, give them at least 4 weeks to write it so they do not feel rushed.
Internships Everywhere Else
Most internships have relatively late deadlines, accepting applications into March, April, and even, in some cases, May for summer. Unlike OCR, it is probably best to start applying in February or March for a summer internship in DC.