I came up to a coworker and asked how long it would take him to complete a task for me and whether he'd be able to do it within a few days. “Sure, that'll be quick and I can probably do it. But I need to ask by team leader.” Excuse me? I would expect that answer from a 7-year old, having to consult his mom for allowance to go out and play, but a tall man in his late twenties is something completely different. Why aren't you in charge of your own work?
If you're dreaming of making any sort of career beyond line employment, then you need to start thinking for yourself. Of course you report to someone and of course he or she will be handing you over assignments, tasks and projects. But you have a mind of your own and perhaps an agenda for yourself as well. Ask your team leader, manager or whoever else is above you for goals - descriptions of areas you should head with your work towards, and don't accept tasks or todo lists. Obviously you can't tell your manager to go to hell with his orders, but what you can do is to analyze what you received, come up with your own way of getting there and propose that back.
The difference is profound. It's not about rejecting orders, but about making your own plan. “Boss, I'd like to do it this way. It'll let me achieve A, B and C on time. And there's this other task a colleague asked me for. I'd like to do this tomorrow and shouldn't impact any other goal and deadline I have. Is that fine?” Of course it is.
If you read Stephen Covey's 7 Habits of Highly Effective People, then the above should remind you of habit 1: be proactive. Very true so, because that's the very same thing. I just can't stand the whining of people who are continuously dissatisfied with their work assignments, yet when asked about what they do to change their situation, claim they have no influence on what's coming at them.
You do. The sooner you understand it the quicker your career will take off. Don't ask for permission. Act.