As someone who made the mistake of spending thousands of dollars on a new idea before, thought I'd pass on some of my thoughts.
Basically, I would say don't spend a significant percentage of your savings on an idea with the hopes that you'll get paid back with future royalties. Too much uncertainty of success and too long a pay back period to justify risking your savings like that. Your ideas will fail much more often than they succeed, so learn to fail on a budget. Steven Key's "One Simple Idea" is a must read in this area and Edison Nation is an affordable way to get your ideas presented to decision makers.
If you're looking to start a business based on one of your ideas and you're not rich, then you'll have no choice but to spend a chunk of your savings to launch it. Remember, in order to do that you have to love being a businessperson more than you love being an inventor.