Hi Eric,
You are right to be wary of this tactic. Not only would you be creating duplicate content by replicating this statement from page to page, but you would also be going against Google's webmaster guidelines which state:
Keyword stuffing
"Keyword stuffing" refers to the practice of loading a webpage with keywords or numbers in an attempt to manipulate a site's ranking in Google search results. Often these keywords appear in a list or group, or out of context (not as natural prose). Filling pages with keywords or numbers results in a negative user experience, and can harm your site's ranking. Focus on creating useful, information-rich content that uses keywords appropriately and in context.
Examples of keyword stuffing include:
- Lists of phone numbers without substantial added value
- Blocks of text listing cities and states a webpage is trying to rank for
(Bolded emphasis mine) See: https://support.google.com/webmasters/answer/66358?hl=en
Unfortunately, if your client lacks the funding to develop unique content for each of his service cities, then he should not expect to rank for them. In days gone by, the client would have needed to pay for phone book ads that highlighted his service cities. Lacking funding, he would have been out of the running. These days, because of Google's bias towards unique, useful content, funding comes into play when it comes to content development.
Perhaps you can find a good solution for this client in the form of an on-going contract in which you develop 1-2 new pages or posts for him per month at a reasonable rate. By then end of 2014, he would have added 12-24 new pages of content to his website, covering his cities and many of his services. He needs to be convinced of the value of this investment, and if you start with just a few of the cities and he begins getting more phone calls, it's likely he will see that this is an essential investment that is going to pay for itself over time.