I personally know leftists who don't approve blank amnesty - a case in example would be the Labour Party of New Zealand. It is officially a member of Socialist International but if you read their immigration policies the the policy of illegal immigrants Labour sounds much the same as Tom Tancredo.
But not American leftists in general. A general consensus is that the West outside the US is more leftist on all areas except race and immigration, in which the pendulum swings to the other side for the non-US West. Just this week we in NZ got a new foreign minister who is a paleocon on immigration.