It depends on if you go to work for the Senate or House of Reps.
I worked in the Senate for 8 years and my husband currently works for the House. The Red Line comes closest to the Senate side, at Union Station (also where the MARC and VRE commuter lines come into DC). The Orange Line will drop you right at the back door of the Cannon Building on the House side. From Foggy Bottom, if you need to change lines, it's easy to do at either Metro Center or Gallery Place. If you are going to work at the Supreme Court or the Library of Congress, it's six of one, half a dozen of the other which line you use, because they are both in the middle between the House and Senate, as is the Capitol building itself.
Either way you look at it, though, a commute from Foggy Bottom is pretty quick on Metro. ALSO, as a federal employee, thanks to Obama, your commute on the metro line will be paid for, up to $200 a month. You could also bike to work, if you are so inclined, as it is only about 2 miles from Foggy Bottom. It is uphill (to Capitol Hill), but it is a gentle incline and you hardly notice it until you are almost to the Capitol.
My company's website has a great search engine that allows you to look at the neighborhood's via map at street level and shows you what properties are available on the map by a little green house icon. Hover over the icon and a small pop-out shows a photo, address, price, BR, BA - click on it and a full listing opens. Our website is http://www.kangalrealestate.com - click on Property Search.
Feel free to drop me a line if you are planning to come to town and want to go house shopping or familiarize yourself with Capitol Hill. If it's not a terribly busy day in Congress or with his committee, my husband could possibly give you a private tour.
Good luck with the potential new job!!
Kangal Real Estate
The metro via the blue/orange line is the best . Go to http://www.metroopensdoors.com and you plan your route - this site will also tell you about bus routes. If driving, take 395 to Maine Avenue, turn right at the WWII memorial, and left on Constitution (prohibited at rush hour, so you have to go up a block and make the left on C and take Virginia Ave) and then make a right on 23rd street. 25-40 minutes depending on traffic.