How much leeway do I have to leave myself to learn a new language?

I think it depends on the area of the project. While GUI is not hard in Python, any kind of GUI-framework will have a somewhat steep learning curve. If it is a webapp, I'd say go for Python. The added time for learning is quickly gained back by easy of use of the many Python webframeworks.

The big risk is that you will code Python just like you code Java. Many of the things true in Java are not true in Python and vice versa. It will probably make your Python code slow and verbose.

If you decide to try Python, read up on common pitfalls coming from Java, for example: http://dirtsimple.org/2004/12/python-is-not-java.html

My boss's rule of thumb is any time there's a learning curve, it can triple the time to write the application. So, if Java would take you two weeks, then Python may take about 6.

It always take longer than you think.

Try writing a small program doing just a bit of what you need. If you are to write a program with a GUI then make small program showing a frame with Hello World and an Ok-button and see how hard that is.

Python is like baby java, you'll pick it up in a breeze.