On the days around Thanksgiving or during a busy weekday rush hour, is the NEC running at near capacity? I understand the tunnels under the Hudson are but it looks like a solution is being worked on (THE Tunnel), but other than that, how many more people could be carried on the NEC?
First this question needs to be clarified a bit. If we assume that only Amtrak was running trains, then no the NEC is no where near capacity. It's only when coupled with commuter service that capacity issues start to enter the picture.
Now, you've already named one big choke point the Hudson River tunnels, but there are others. First is the capacity at Penn to handle more trains, one reason that in conjunction with the tunnels a new station is being built under 34th Street.
Then there are capacity contraints at Boston's South Station that while not currently a problem, could become a problem as the T adds more trains and if Amtrak also wants to add more. There is also a potential for problems between Attleboro, MA and South Station if more too many more trains are added. Moving south, the potential for conflicts increases on Metro North territory, especially if there are any problems.
South of Penn we have the two track Portal bridge not far from Secacus Junction which is almost at capacity right now, and will need capacity improvements before anyone can really take advantage of The Tunnel. The next potential choke point is Wilmington Del, where things are ok right now, but any substantial increases by SEPTA or Amtrak will start to create problems.
Further south from Perryville, MD to the Gunpowder River could become a problem if MARC ever needed to triple, possibly double, it's current service levels. Then just south of Baltimore things are already getting tight in the tunnel just beyond the station. Part of the problem here is simply the low speeds, so fixing things up to increase speeds would help. But it wouldn't be a permenant solution if service levels continue to increase.
Finally some improvements would need to be made to the interlocking leading into DC, if service levels were to be increased by much more than what they currently are. The speeds across the interlocking are just to slow to keep things fluid with many more trains. Of course going southbound they really can't go too much faster without risking using the station as a bumper block, and we don't need to park another engine in the basement like the Pennsy did with that GG1 many years ago. But northbound things could really be helped by increased speeds.
On a side note, took Metro-North from Stamford to GCT today and the train was PACKED. They really need to add some more holiday trains or add some more cars, if they have any.
Well Metro North is having a big problem right now with flat wheels thanks to the fall leaves. I saw a news report not too long ago that IIRC stated that they had over 200 cars out of service thanks to the slippery rail conditions caused by the falling leaves. They were running their wheel truing shop 24/7 trying to catch up, but even then I think that they can only fix about 18 cars per day, so there is a big backlog.
All that said, they probably should have tried to run a few more trains than what was planned even before they lost all those cars.