It depends on the country and how strict the tests are there. Here in the UK it would be very difficult to do so in normal circumstances, the test is quite difficult and it would usually take months of lessons to pass. I've heard that the test requirements are a lot easier in the US though.

And it depends how much time you have to learn before your deadline too. When I did lessons I had a one lesson per week of an hour or two, and a few sessions here and there where I'd go out with my parents and practice. The general rule was something like 20 hours of lessons to be ready for the test, and for most people that would mean 10-20 weeks. You can of course fit more in though, depending how best you learn. Driving for long periods takes a lot of concentration, especially for a new learner, so it's probably not a good idea to try and squeeze in more than a couple of hours per day.

There are some "intensive" driving courses where you'd basically spend a week doing constant lessons and practice and they claim to be able to get you ready to take a test in a week. So it's definitely doable, but the less time you have available, the more time you're going to need to squeeze practicing in that time.