The nominal max speed of Amtrak trains is about 79mph [1]. When I was traveling up I-57 in IL (speed limit 70mph), the Amtrak train was going almost identically in speed.
Most of the class I railroad track was built to handle high speed (by early 20th century standards) traffic, so trains can generally reach 70-90mph (although not so much in suburban or mountainous areas) with little modification. The difficulty is that there's no economic reason to push freight trains to high speed, and mixing higher-speed passenger and low-speed freight creates scheduling conflicts, so passenger speed tends not to hit its top speeds.
[1] On freight track, that is. The NEC, which is all passenger traffic and all-electric, has higher nominal speed: even the "slow" NE regionals will hit 100mph on the empty track in MD.
To add to this, the FRA regulates track speed based upon condition of the track and some other requirements. Track condition is typically quite good (rail companies really want to avoid derailments), but one of the biggest impediments is grade crossings. The faster the track, the more extensive protection needed to keep trains and cars separate. Table 42 [1] here gives the requirements. Most of the mainline track is Class 4. You'll notice to hit 125 mph every grade crossing needs a full barrier between the car and train. And faster that that, complete grade separation (ie, bridge). US rail was not designed with this in mind and while they close a grade crossing any chance they get, they're still a major hindrance to high speed operation.
Most of the class I railroad track was built to handle high speed (by early 20th century standards) traffic, so trains can generally reach 70-90mph (although not so much in suburban or mountainous areas) with little modification. The difficulty is that there's no economic reason to push freight trains to high speed, and mixing higher-speed passenger and low-speed freight creates scheduling conflicts, so passenger speed tends not to hit its top speeds.
[1] On freight track, that is. The NEC, which is all passenger traffic and all-electric, has higher nominal speed: even the "slow" NE regionals will hit 100mph on the empty track in MD.