Taylor Mallory Holland at Content Standard wrote this insightful article how tight deadlines can have both a positive and a negative affect on creativity.
From her article:

Dr. Richard Boyatzis, a professor of organizational behavior, psychology and cognitive science, explained his team’s findings to The Wall Street Journal:
The research shows us that the more stressful a deadline is, the less open you are to other ways of approaching the problem. The very moments when in organizations we want people to think outside the box, they can’t even see the box.

Taylor offers the following advice on how find the right balance:

Ditching deadlines isn’t the answer, nor is sacrificing quality for the sake of speed. But how do we find a happy medium?
For leaders in creative fields, the lesson here is to set flexible deadlines whenever possible—to leave some wiggle room in case good ideas take longer than planned. Consider breaking large projects into smaller tasks with their own deadlines. This not only prevents last-minute stress and overwhelm for workers; it also gives you good opportunities to check in and to offer support and feedback.
As Laura Vanderkam points out in her Fast Company article, it also helps to know your team members and set expectations for individuals. She says that while some people are good at meeting deadlines, “Others need more hand-holding and frequent check-ins. They’re not bad people, they’re just different people. Good management means getting to know the people you’re working with, and using deadlines as one tool in your kit for getting good work out of them in a timely fashion.”
While an understanding and flexible boss is certainly an asset for creative workers, individuals must also take responsibility for getting the job done—for thinking as creatively and as quickly as possible. This requires commitment and proper planning so we can give ourselves the time we need, rather than rushing at the last minute and stressing ourselves to the point of writer’s block. It also means learning how to get in the “creative thinking” zone when we need to be productive, not just when the moment strikes.
For scientifically-proven ways to be innovative and efficient, read “7 Productivity Tips to Boost Creativity on a Deadline.”