The other side...
I was on the other side of such a situation. I was the customer.
Major OS upgrade of a HP-UX server. As the clueful customer who had sysadmin background, I asked for three days to do the OS upgrade. HP professional support told me I was ridiculous, it'd be done in 4 hours, maximum. We convened everyone, including the lead "sysadmin" (who actually had no sysadmin background, but I was helpfully training because they were a good problem solver and learned well) to do the upgrade -- only to find out we had a known bad version and we had to abort before we began. The next chance we had was the next week Thursday at noon...
The sysadmin was a professional organist and was playing at a wedding that Saturday, even if they didn't have a job the following Monday. We get together, confirm we have the good OS disks (I think these were DVDs, but I could be off, it was 2-4 disks total). Computer hangs on boot after upgrade. No recovery.
Professional services looks at it, shrugs and says "Wow, we've never seen that before. Good luck with that, good bye!"
We pull out our HP Ignite image we carefully took right before we started, against Professional Service's advice, rebuild the system from that, verify it works right and start figuring out how to recover.
Friday afternoon, the sysadmin flies home on their flight, we haven't figured out how to solve the problem. The sysadmin's boss called another person and said "Here is a one-way ticket to $CITY. You are there to represent the sysadmin team." The person had no sysadmin background, didn't know a lick of HP-UX (or even any close enough Unix to be useful), but they were there and not allowed to leave until the problem was solved.
Meanwhile the application vendor's tech rep and myself (in theory just an application admin) are doing all the technical work of figuring out what could be the problem, what to try next. I'm briefing VP level leadership every four hours on our progress, or lack thereof, so everyone knows exactly how bad the situation is.
Saturday night, 60 hours into our upgrade effort, working 20 hour days, we found the source of the problem -- from the first line tech support at HP. None of the second or third liners knew the problem, but this first line tech support person rattled the solution off immediately, and it fit perfectly the symptoms. We kicked that off and 12 hours later, we had the OS upgraded, the application updated to use the new OS and everything working fine. I'm told the poor sysadmin with the one-way ticket actually did get a ticket home before Tuesday.
Total time start to finish: 72 hours. Exactly the three days I said I wanted for the change.