I will say a lot of their travel and either apartment lease or hotel is paid for. There is a certain fund each personal office gets to cover things of that nature. However, to your point D.C. is a stupid expensive city from living here to food. In part due to the pay Member of Congress often are wealthy people who can afford to not make as much or they serve for X years before they go into the lobbying space because they didn't make anything for whatever amount of time they served in Congress.
They as in Congress only within the last couple of years increased the amount that a staffer could get paid and the reason was the pay discrepancy is stupid. I've been here ~2.5 years and my salary was $65k and that was with me making "good" money for my position as most make $60k. It is hard to justify the stress and hours the more you look into it and to know that for most staffers once you hit the $80 to $90k level you really platue... retention is hard for the best most experienced Congressional Staffers.
I have friends around my age with less on their resumes that because we know the people that we know and understand the way the government moves are making $175-$200k right now.
Pay alone though wouldn't fix it. Our benefits are way way way behind the private sector and our health insurance isn't good at all but is still stupidly expensive. We get free therapy at the Office of Wellness but really that's about it.