I went to DC this past summer, and trust me, you wouldn't be able to do some of those things. We only got to see the White House from waaay far away at the gate on the front lawn, and there IS no statue of Washington. Not at the Washington Monument anyway, so I never saw one. Jefferson's statue was REEEEEEALLY BIG though. ;)

And don't ask the money people if they give out free samples. I'm sure they've heard that line more times than I care to count, and they'd get PISSED.

I do however recommend visiting the Smithsonian, as that was AWESOME (though I wasn't able to find the Indiana Jones whip and stuff), if you ever do get to go. :P