It is 2.8 miles and will take you about an hour to get to the White House by walking. From Lincoln Park You can also go to the Eastern Market metro station. Then ride it for six stops on the blue, orange, and silver lines until you get to the Farragut West metro station.
If you take the nearest metro stations (Eastern Market, Potomac Ave) then its 6-7 stops, which isn't bad timewise. Possibly a 10 minute drive, but it wouldn't make sense to walk from there unless you really enjoy walking.
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