[mikeash]

This worry about "waste my one phone call" makes no sense.

You're not obligated to talk without a lawyer. The police won't give you what you need to find a lawyer? Fine, just don't talk. If they're stupid enough to say, "you wasted your one phone call, no lawyer for you" then just sit there.

The legal system is run by humans and doesn't generally have silly gotchas like these. There's no such thing as, "you couldn't find a lawyer in ten minutes with one phone call, so you don't get to have one, gotcha!"