Definitely concur with checking AutoSlash. I've found good deals through them when I haven't been able to get a corporate rate. My lately go-to for low-cost weekly rentals at DCA has been Sixt. Depending on timing/coupons you might be able to find them in the $250-350/wk range.

In terms of experience; DCA is my number one pickup location, and here is my opinion on the different agencies at the airport. Ranked in order of who I prefer (indifferent to cost)
- National: With Emerald Club (EA/ES) membership is almost always quick and easy and cars usually exceed my expectations. Returns are fast - and excluding automated fuel readings, I've never had an issue with false damage/incorrect fuel
- Enterprise: Same as National, but slower pickup process, cars usually meet (instead of exceed) my expectations
- Alamo: Same as National, pickup fast if you checkin online, but cars have been higher mileage than I want
- Sixt: Cars have always exceeded my expectations, never had issues with fuel or false damages (despite the bad reviews I've read). With a Sixt Express account and online checkin the process to pickup a car is way slower than I want, but still significantly faster than having to wait to pickup at the desk. As a word for caution - I head the agent ask others if "they wanted enhanced insurance, or just the basic"... I hate this question because it's a trap to get you to decline the full package but still accept their CDW.
- Avis: Eh... it's offisite. Avis preferred is ok in my experience (fast enough) - but you'll struggle to get me off-site unless the price is astronomically lower. Never had issues with damage (before the off-site move). Fuel has been a hit/miss as a majority of their cars were auto-reporting, which is hard to fill up perfectly.
- Hertz: Mediocre cars, long waits (out of stock), slow exit process. No issues with damage, might be because the cars have all been 30k+ miles and former lease returns.
- Budget: Avis, but slower pickup process.

Haven't used Thrifty or Dollar at DCA.