Casey Mulligan's post, on the liquidity trap argument, is spot on. Here's another simple thought experiment. Let's say that, for reasons of technology, currency disappeared. All transactions would be made with POS or cell phones, backed by interest-bearing assets, in one form or another. You might think that's unlikely today but it's at least possible in the future. In any case, it's a thought experiment.
In this world there would no longer be a trade-off between currency and interest-bearing assets, as we find in traditional Keynesian models. There would be no substitution out of one and into the other and there would be no swapping of currency for interest-bearing assets.
What would the macroeconomics of this world be like? Would the AD curve slope upwards? Would increases in employment be contractionary? No and no. It would only be slightly different from our current world, a point Kroszner and I made in our book Explorations in the New Monetary Economics. It just doesn't matter that much if you pay for your retail transactions by leaving a five on the counter or by using a credit or debit card backed by interest-bearing assets.
Liquidity trap arguments are themselves a kind of trap. The theorist finds one situation where the traditional marginal equality between various rates of return is disrupted and people stand at a corner for one of their portfolio positions, namely cash vs. interest-bearing assets. The model then has consistency requirements, in the form of interrelated mathematical equations, which "spread" the counterintuitive results across the entire economy. But that's assuming the model is a more powerful description of reality than it actually is. It's better to side with common sense instead.
Addendum: Arnold Kling offers related comments.