Will we ever see a "within 24 hours" shipping time for the new Mac Pro, or will there always be a +/- 60 day lead time on orders for the life of the product?
It isn't 60 days now. Currently creeping up on the middle of March and the online Apple store (USA version) is still showing "April". So it is more than 30, but less the 60 days at this point. ( even if something ordered right now misses April 30th and slides 6 days into May it is still less).
Fixed configurations should get to "24 hours" in a couple of months. BTO configs may never get to "24 hours". "24 hours" is highly suggestive that Apple decided to build the machine before you ordered it. For the overwhelming vast majority of possible BTO configs I don't think Apple is going to shift to making it before you order it. It won't be months or multiple weeks, but hours isn't likely.
I'm wondering if Apple is "ramping up production" and will eventually be able to meet demand, continuously and without hiccups, or if they have maybe made a gross miscalculation with regard to their US manufacturing plant's ability to produce machines.
More likely Apple calculated what the average demand would be over the system's production lifetime ( 10-15 months) and provisioned a contract to cover that. Apple will 'catch up' as monthly demand falls below designed max monthly capacity. When the machine gets made is being time shifted, not particularly whether the machine gets made.
When 3rd party SSDs show up that will slightly shift more demand into standard configuration systems. ( as customers will buy and then customize). That apparently isn't going to happen until Summer.
One thing that Apple appears to have goofed on is standard configurations. They went from 5-6 down to just 2. ( Granted dropped dual CPU offerings but still 6 -> 3 would have made more sense). The ordering tracking spreadsheets is suggestive that not having a "good, better, best" line up was mistake. They should have had a "best" ( 6 core , bump in SSD , D700 ) configuration that could have been bought off-the-shelf (or more specifically; out of the warehouse ). If they would have made a fair amount of those before launching they would not have fallen behind as far as they have. There still would have been a delay ( just-in-time manufacturing and relatively high initial demand bubbles are a mismatch).
The expected number of BTO orders was probably lower or was in the "unknown" category. If it takes until May/June to catch up, then it was far closer to "unknown".