Invoking the lazy web bicycle mechanic

When it’s cold out, as it has been in Tucson the past handful of days, the shift levers on my bicycle don’t catch; I end up unable to shift down a gear on my rear chain ring and unable to shift to higher gears on the front chain ring.

So, lazy web bicycle mechanic, Is this something I can fix myself after buying a specialized tool that I’ll never need again? Or, should I just go and get the bike that tune-up that it desperately needs, anyway?