It is worth mentioning that the Platinum Chip was printed in Sunnyvale California and the wiki implies that is also where it was found. A bit of creative story telling could explain why House might be so desperate as to search DC, but it is going to be a bit of a stretch.
Ah, ye of little faith.. :)
House didn't know for sure it'd be in Sunnyvale, even though it was printed there. He spent a huge amount of money - somewhere around 800,000 caps in 2280 - over a roughly seven year period searching for it. And we're talking about what, back in 2077, would likely have been a wartime defense project.
There's lots of reasons why the chip might be in DC or elsewhere. The software may have been developed there, only the final printing to happen in Sunnyvale, and perhaps the final fabrication didn't happen in time before the bombs fell. DC is a long shot, but so is the entire search. Basically a poker chip lost for 200 years somewhere in the desolate nuclear wasteland.
The most likely DC scenario I see is that it may have ended up in Brotherhood of Steel archives. Back in the day, they had a strong presence in the Bay Area, in San Francisco and almost certainly down the road at the Fallout version of Livermore Labs, where FEV was created with West Tek. Livermore is only about 25 miles from Sunnyvale (I live about an hour from both).
So let's say that, as the Brotherhood-NCR war starts going badly for the BoS, the West Coast elders see the writing on the wall and start shipping more of their recovered prewar artifacts to the East aboard BoS airships (much as the Enclave did with their assets, and for much the same reasons). Not to mention, keeping it out of NCR hands. There's a reasonable chance that the Livermore recoveries could be among them. They shipped the last Maxson scion to DC, after all; it was only somewhere around 2276, shortly before the Outcast desertion, that their supply lines were finally cut by Lost Hills.
Sure, the chip ended up in Sunnyvale after all. But House spent a LOT of money over years chasing what amounted to dead ends. With the Brotherhood out there doing their thing, the DC Wasteland is certainly full of promising dead ends.
I have some thoughts about where the trail leads in DC from there, but I'll get into that tale in the mod itself.