Well, I haven't had the time to dig very far into the ConLaw research to get the answer to this, but I did take the time to kick it around with a buddy of mine who is an attorney and a former probation officer. He is of the opinion, & it's an opinion that I trust, that the US Constitution* does not require that jails allow any phone calls upon arrest. He thinks that's a myth. That said, we both agree that as a matter of courtesy, most jails will allow you one call. It may simply be that the only thing required by the federal constitution is the prompt first appearance.
Sport45 -- Sort of. Unless your wife or the other person that you call is an attorney, they're not entitled to represent you in court. I've gotten enough calls from family members to know that around here, calling family members is permitted*. Other than that, it's a good plan. A family member who's not in jail can make all the calls that they want to. I'd suggest making sure that your wife or other significant other has all of the important phone numbers already programmed into his or her phone.
*=YMMV in your jurisdiction. State constitutions may contain more protections or require different things than the US Constitution, as long as they do not violate the US Constitution.
I'm a lawyer, but I'm not your lawyer. If you need some honest-to-goodness legal advice, go buy some.