For India, free trade means free movement of services workers in an out of the U.S. Indian businesses are trying to convince lawmakers to see this relationship as mutually beneficial, with both gaining from the benefits of trade. The CII says 35 Indian firms in all industries have created some 60,000 jobs in the U.S.

But trade relations, at least as far as India's IT industry is concerned, is on an unsteady course. Congress recently increased fees for H-1B visas by $2,000, and Indian IT companies are facing increasing , said Som Mittal, president of the National Association of Software and Services Companies (NASSCOM), India's leading IT industry group.

Indian firms are being hurt by "excessive denials" of visas and burdensome requests for evidence in support of visa petitions, issues that immigration lawyers in the U.S. have also complained about, Mittal said.

"At a time when we are opening up borders for trade, the free movement of people does become a big irritant," Mittal said. The problems with the visa are coming at the same time that U.S.-India trade is increasing, he said. "These issues are becoming very sore points in discussions."

Proponents of offshore outsourcing argue that the ability of U.S. companies to shift work to lower-wage countries allows those companies to reinvest the savings and create other jobs. Opponents of offshore outsourcing say it leads to job losses and a discouraging future for IT, particularly as more complex work moves offshore.