See the reflective piping right under my rack?
It weighs less than a pound, it's tiny, it COULD easily go under my seat (I have it under my rack so my work shoes fit under my seat easier), and it holds a spare tube, a Park Tool MTB-3, tire levers, a spare SRAM PowerLink for chain repairs, tire patches, and the rubber cement and scuffer that came with the patches.
You can see my cheap (but worthy) frame pump under the rack on the other side, too. It's the silver/black bar.
Do yourself a favor. When you go to the bike shop tonight, instead of spending money having them fix the flat, spend a few bucks and get a little bag and some emergency gear. Hell, if I bought $50 worth of stuff (which is about what the tube, patch kit, levers, frame pump, MTB-3 tool and bag cost me) from my bike shop, they'd probably patch my flat for free right there on the spot.
For things like tightening allen screws, adjusting stuff in the middle of nowhere, or making impromptu repairs on the road, the MTB-3 is a great tool. Similar ones can be purchased for less but I got it for its tiny size and warranty. When your bike goes from cold to hot and cold again day in and day out, things tend to wiggle loose a little faster. I like knowing I can tighten things up on the fly.