•What do you motivate your team in times of time constraint ?

If I rephrase this question, it might read like "What do you do to motivate your team in time of constraints". 

- First we define the word 'constraints'?  Here I take it as financial constraint as it is the most critical element that demotivate anyone.  Employee expect annual increments, bonuses, overtimes etc. etc. and once it does not happen, they get demotivated.

Culture of any organization counts a lot in times of financial constraint.  Best thing is communication, both at horizontal and vertical levels.  If you are working in such organization, task might be easy but otherwise, you need to work hard to retain the talent.

You can also try to get your team and yourself involved in learning new things.  There are many sites which offer free online courses that you can join together and have brain storming sessions.  Try any of them (www.coursera.org and https://www.futurelearn.com/).

Time is money. This is the kind of world we are living in. The work is considered to be effective and efficient only if it is completed within the time limit. Being the project manger i would try to make realize my subordinates the importance of the time constraint that we have and also how it would benefit us in future if we can tackle this now. How it would raise the efficiency bar of the team and how better responsibilities would follow in the coming days.