One thing to note about the DC Metro (as opposed to NYC Subways and many other city subway type systems) is that the rates are different during peak times (before 9:30am and 3-7pm) AND there are different rates depending on how far you travel (not to do with changing trains but the distance from your start point to your end point). They do have machines by the exits should you not have enough $ on your card, so you don't have to worry about being stuck (like the sort of famous song about the Boston MTA ;)).

They do offer a daily or 3 day pass, but you'd have to look and see what your plans are - if you are only riding in and out each day, it may not be cheaper than just paying the individual trip rates.

As I remember, you can add extra money in fairly small amounts, so you should be able to wind up with fairly little on a card, if you don't want to have to send it in as mentioned above.

Also, while looking at that info, happened to see that there are four locations that offer some (limited) multi-day parking (up to 10 days), one of which happens to be the Franconia station mentioned (limited for that meaning 15 to 17 spots, out of about 5,000 total, so who knows if one would be available when you needed it). The other 3 are Greenbelt, Huntington and Wiehle-Reston East.
So, pretty minimal (since they say 44 stations offer parking), but there is a small chance it would work out.