Actually no, not that I can remember. There is no real 'timed' quest in Skyrim that you could potentially fail because you took your sweet time, you can do everything at your leisure as far as I can tell. Even if the quest-NPCs literaly tell you "HURRY, WE NEED TO GET TO DUNGEON/PLACE/TOWN ABC, RIGHT NOW! OR XYZ WILL GET AWAY!", you can decide to do as much lollygagging as you want, because the said npcs will patiently wait for the player outside the location. Even if takes you months. Quite hilarious in some situation when you think about it ...
I think we should not get to hung up on the "urgency" though, I think no one here expects that all and every quest in Skyrim should have a timer clicking in the background. The problem is just, that a lot of the quests in the game are trying to create some kind of urgency, well because it ads to the drama! And drama is a good thing in quests, right? Even if it is just fake, because you never feel any consequence. However, 90% of the Skyrim quests always use the same blue print. Go there, do this, kill that, collect this, return, rince and repeat. It. Is. Always. The. Fucking. Same.
The best quest in my opinion, was the task you got with the Thalmor breaking into their embassy. Not only could you actually use some thief skills here to great effect, and roleplay a 'little' but it was a quest that created urgency on it's own, without always telling you that you had to do it now, it also required the player to step out of his role as adventurer for a moment and pretend that he was a noble to get access to the embassy. As far as Skyrim quests goes, it was one of the better places. Sadly, it was a rare moment. I don't have a problem with this Sandbox experience, but as some already mentioned Gothic 1 and 2 did it already 2 decades ago, and much better at least as far as the story and quests goes.
By that logic, why does Skyrim even have a level up system? What kind of toolbox withholds the best toys?
The first time I played Skyrim, I played it how it was supposed to be played, and boy was it a snooze fest to level up skills. But each new game, one of the first things I do is to level up every skill and giving my character the best items. Skyrim, is simply way to much of a useless grind in my opinion. I am not spending 5 hours of crafting and enchanting daggers like in some shitty MMO, just to get 100 points in smithing or what ever. Though, the whole level up and combat system of Skyrim is such a shitty system ... the first time I played the game, I had some serious issues for a couple of hours, because it seems no one at Bethesda thought about what happens when you decide to level up mostly alchemy, enchanting, smighting and/or merchantile and other non-combat skills. The whole game doesn't even assume for a moment, that someone would NOT level up combat skills.
I still think that who ever came up with this skill system should be kinda slapped in the face. Or forced to go trough brewing/smithing/crafting 1000 items every day.