I don't think so. At this point Americans don't seem to care. In ripe cities, they see many immigrants from different countries many of who are GC holders or citizens. Btw many of them came here a couple years ago on the same h1b visa, so not sure why only Indians should be looking at it differently?
The fact is America always needs high-skilled labor, to keep its economy at the No.1 position. They're however, not ready to reward that labor so readily.