brass polish alternatives?

I need to polish a very small amount of brass but I'm too cheap to go out and buy some tarnish remover.

Any suggestions on household products (preferably non-toxic) that might make a good substitute for brass polish?  

Toothpaste, vinegar and salt, lemon and salt, all remove tarnish

toothpaste!?!
neat!  

Cut a lemon, peel it, take a chunk of peel and sprinkle salt on the inside of it. Rub the brass with it. When it's clean enough, turn it over and rub the exterior of the peel on the brass, the oil protects it.
If the brass is really grubby, leave a bit of the pulp in the peel, if it's not, you probably don't need it. Too much acid eats the details on your brass down if you do it too often.

Liz uses ketchup on copper. Works super and you almost always have some on hand.
I suspect it will work well on brass.

Agree with the lemon suggestion - can also used powdered citric acid the same way since many home preservers have a bag of this hanging around.

I'm going to agree with Thomas on the ketchup. A customer restoring an old Harley asked me what to use to clean a brass carburetor. I suggested the lemon and salt and mentioned the ketchup. He opted for the ketchup and the carburetors came out beautifully.

Sounds like you're wanting something acidic (citric acid, lemon, ketchup) and salt.

This makes sense to me, because what you're doing is removing the patina by eroding it with acid and salt. I've recently been learning about mordants and metal-based wood stains the common recipe is salt and vinegar.

Nicole is right. To get the grime off you need to use an acid to remove the patina.
Just how dirty is your brass?
I bought a beat up old house years ago. It had a 2 foot piece of brass railing in a bathroom. It was used as a handicap bar to get into the tub. Probably installed 50 years ago before there were handicapped items. It looked like it had NEVER been cleaned. It was black! Seriously black! Tried a dozen products, scrubbed it till my knuckles bled. Nothing worked.
Until I found 'Barkeepers Friend Cleanser'. Made a paste with water. Wiped it on. 15 minutes later scrubbed it off. And the brass was beautiful! With no patina left it is the color of solid gold! The natural patina comes back after a few months.
It has an abrasive agent but the main ingredient is oxalic acid which is also in spinach, brassicas and rhubarb. It's a lot stronger then lemon juice. I use it most of the time now. Works great on stainless steel, the stove and lots of other things. And I too use ketchup on copper.
Get's the job done so I spend lots more time in my garden.

Not brass, but copper:  A bit more than a decade back, I remodeled a house with literal sheets of copper covering the entire attic. The copper was badly corroded and tarnished. I bought a gallon of taco sauce from a restaurant supply and tried it. In mere seconds, you could see the sauce do its magic without any scrubbing. The copper shown like new