2 Channel USB mixer - are you thinking of an Audio/Midi USB interface? They do allow more than one input normally but essentially they are analogue to digital converters. These (at entry level) usually allow you to input two devices - e.g. one mic and one guitar.
I can't actually help you as I don't have one to spare but if you are thinking of a USB mixer then I guess you are looking for something like a Tascam US-122. They retail at about £120 but I'm sure you'll get one for much less 2nd hand on ebay.
If it really is a mixer that you are looking for then you'll be hard pressed to find a 2 channel (except for a passive device) mixer these days - I suggest you look out for a 4 channel mixer (they start at 4 channels usually) - these retail new from about £65 so there should be something cheaper on ebay. I use a Behringer. This would go analogue (mini-jack) into you PC/MAC though not USB.
Now a mixer with a USB interface as well as an analogue interface - that would set up back a lot more.
Hope this helps - ignore me if I stated the obvious.
When you say a two channel mixer do you mean that you want it to have two mic channels? For example, the photo below is of my Behringer 502 mixer, it has 5 inputs, but only one of those is a mic input and that doesn't have phantom power.
I should have dusted it before photographing it.
Without phantom power I'm limited to using a dynamic microphone such as this:
This mixer is the cheapest I know of, but is not USB and I don't know of any cheap two channel USB mixers. Behringer do make a USB converter that converts an analogue stereo feed into a digital signal and it goes for about £30: U-CONTROL UCA202
This could be plugged into the output of the mixer above to give you a possible solution.