I would go with Notre Dame even if you want to work in DC. Almost every student at GW is going there over some other school because they want to work in DC - why else would you pay such a huge premium when there are similar options for a fraction of the price? Thus, when it comes to OCI, the GW student will be competing against almost all of their class - the supply of applicants far far outweighs the demeand from the firms because firms want diverse summer classes. In contrast, your classmates at Notre Dame came there, for the most part, for the reputation of the school, not so they could get a job in Indiana. They will be looking to go all over the country, meaning that a relatively small percentage of your classmates will actually be trying to end up in any one market. This greatly tilts the supply side. For example, the DC firms want a Notre Dame student, just like they want a GW student, a UVA student, a W&L student, G-town student, a Harvard student, etc. So, the supply/demand comparison is much different, and I think better, for the Notre Dame student, plus you're not paying a ton to still live a 40 minute metro ride from school.
This is, to put it mildly, not very good advice. Do a search of the NALP directory to find how many firms from DC interview at GW, and how many interview at ND. I can assure you that many more interview at GW.
Maybe a student at the top of the class at Notre Dame will have some choices in DC, but a median student from Notre Dame will not be getting any jobs over a median student from GW in DC, simply because the firm wants a "diverse class".