Immigration Services backlogged as thousands wait for Green Cards Statistics show that Houston has close to 50,000 immigrants waiting for a Green Card. And Houston has one of the longest waiting periods in the country. An upcoming federal deadline set to shorten the waiting period to six months or less by the year 2006 has Immigration Services backlogged. opyright ©2004Houston News Channel, L.P. d.b.a. News 24 Houston