That's a big problem. Firefox and Chrome these days support debugging source mapped files. However, I'm running through two source map steps: TypeScript to JavaScript and JavaScript to minified JavaScript. For whatever reason the browser debuggers don't work that well with this setup. They're buggy and make the browser very slow. I often do have to resort to "console.log" debugging. On the plus side I'm always running code like it's run in "production", which will make it easier to catch any bugs resulting from minifying.
I use Webpack with a similar setup (CoffeeScript->JavaScript->Minified) and I didn't notice any issues. Source maps stop working when using Webpack's hot code reloading, but it's a price I'm willing to pay.