The Channel Tunnel is only 31.5 miles long vs 230 miles (driving) from New York to DC, but having an access shaft every 30 miles or so wouldn't be that bad.
I'm not sure how you'd deal with the vacuum issue though - I guess doors at regular intervals that can be sealed, so a section of the tunnel can be bought back to atmospheric pressure, and the emergency doors can be opened between the car-tunnel and tunnel-emergency tunnel.
The Gotthard tunnel has them about every half mile, but the Boring Company will use smaller diameter tunnels where smoke and gas spread faster, so they'll probably need them more tightly spaced -- say, every quarter mile. And they'll use separate tunnels for each direction of traffic. So that's three tunnels plus 230 x 4 x 2 = 1,840 cross passage tubes.
This is all technically achievable, but the Boring Company's vision is all about cost.. building tunnels 10X cheaper. This is, I think, at least as great of a challenge as getting government approvals to dig very deep.
How do you make a very long, very deep, narrow-diameter, elevator-accessed tunnel safe from fires and toxic gas releases? You can make it a vacuum but then what if you have to escape a vehicle? How does this thing not become a death trap in the event of a fire?
Fire is the number one cause of fatalities in tunnels (remember it's the smoke that kills). Tons of engineering and expense goes into trying to devise shelter and evacuation solutions.