If you've taken the time to develop your goals and objectives, need statements, organizational history statement, and budget, you might just be able to turn the grant application around in a week. Otherwise you may have to wait until the next funding cycle.
How can you determine the foundation's funding cycle? You may have to do a bit of investigation to find out what a foundation's cycle is--look at their IRS Form 990, annual reports, and past grants awarded. You can call the foundation and ask for its funding cycle. It's a great question to get a conversation started and begin developing a relationship.
It's pretty obvious why deadlines are important. Deadlines mitigate procrastination. They motivate us to get something done. They promote focus and productivity. Deadlines and funding cycles are your friend. They help you stay on task and plan for the future.