Import people or export work' was a stark fact conveyed by Nasscom to a top US official and several Congressmen at the time of the first 'outsourcing backlash' in the early 2000s. It reached a crescendo in 2003-04 and was an important issue in that year's US presidential election campaigning.
It did end soon after polls, as more people understood the win-win India-US IT relationship. Consequently - despite continuing battles - things on the visa front did become easier for Indian IT companies. The vast improvement in political ties post-2004, too, helped.
