what is an estimate of the number of 'seats' (service representative positions
) in call centers and contact centers in the United States?

Hello cb1066-ga

Hopefully the following excerpts will give you an indication of the
numbers and approximate an estimate - from call center news:
- "3% of the US working population is currently employed in call
centers, for a total of 1.55 million agent positions in the US call
center market. At a 6.5% CAGR, the number of agent positions will grow
to 1.979 million by 2002.
Datamonitor, 1998."
-"There are approximately 7,000,000 agents now working in 70,000 call
centers in the US, with an annual growth rate of up to 20% in agent
positions.
Davox, citing F.A.C./Equities, 1998."
- "The rate of growth in the number of call centers is slowing, from
4% in 1999 to an estimated .8% in 2003, attributed to both maturation
and consolidation within the call center industry.
Datamonitor, 5/99"
- "There are 69,500 call centers in the US, growing to approximately
78,000 in 2003.
Datamonitor, 5/99"
from "Industry Size" call center news
http://www.callcenternews.com/resources/stats_size.shtml
- Excerpt from section 2.1 CALL CENTER MARKET OVERVIEW page 7 also
quotes the above figures and other useful data about the industry.
"At a 6.5% compound annual growth rate (CAGR), the number of agent
positions in the U.S. is projected to grow to 2.0 million by the year
2002."
from "ITSC Information Technology Support Center" sponsored by the
U.S. Department of Labor  "The Evolution of the Call Center to
Customer Contact Center" Feb 2001 version 1, PDF file (requires Adobe
Acrobat reader to read... right click link below and download to your
local drive as it will take a while to open in your browser - file
size 512k )
http://www.itsc.state.md.us/ITSC/delvrbles/C-4-1/Call_Center_Evolution_C4_Final.pdf

Search Strategy:
call center staff employed states OR america
://www.google.com/search?q=call+center+staff+employed+states+OR+america&hl=en&lr=&ie=UTF-8&newwindow=1&start=10&sa=N
statistics 2002 "contact centers" staff employed states OR america
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&newwindow=1&q=statistics+2002+%22contact+centers%22+staff+employed+states+OR+america

I hope that helps,
if you need clarification of the answer, just ask.
Kind regards
lot-ga

Very pleased: excellent research!!