The problem with that quest shouldn't be stamina, because you're just chilling out in a house. It should be easy to have high stamina there.
It's what Adrenaline said: Your character doesn't have the skills to pickpocket or persuade anyone. That's an early Thieves Guild quest, but if you don't have the relevant skills it's next to impossible. If your character is good at combat but not thieving, your options are to murderer them for their keys (if you taunt them to provoke a fight, it's technically not illegal to defend yourself!) or do it later when you've paid someone to train you in Sneak or Speechcraft . (You can also train Sneak by toggling Sneak on and standing in observation range of a character but in a position where you character will sometimes briefly successfully enter Sneak status, if you want to do it organically. But the chance of successfully entering Sneak status is so low at low skill levels that you're better off paying someone for at least the early levels.)
But, basically, it's not like Skyrim where any build can do the Warrior, Wizard, and Theives' guild quests and a character who can't cast a spell will become the head of the Wizard's College because he's the protagonist. If you're a warrior, you're going to hit a brick wall with quests asking for skills you don't have unless you start to seriously train them. (Although, like in this case, sometimes this can be solved by being using the thing you are good at, melee combat, to do a murder instead.) There's a Wizard faction in Morrowind, and their whole town is designed to be inaccessible unless you can fly, for example. There are enchanted objects that you can find (or make) to help a warrior get around this, but it's easier for a magic user. This early thief's guild quest is a similar situation. Maybe at some point you'll be able to do this the right way, but probably not now without a lot of savescumming for the best possible outcome.