Immigration can be a blessing or immigration can be a curse. The difference is often a question of selectivity. It's a question of who those immigrants are and what their values are. Most nations have been shaped by migrating populations, for the better or the worse.
Sometime around the 19th century American Democrats discovered that immigrants were more than just a useful source of cheap labor, but that they were ideal for farming out and creating a power base. Aaron Burr, who would go on to become the Democratic Vice President under Jefferson, kill Alexander Hamilton and plot a Northern secession and a takeover of Mexico, got his first taste of power when he used a fraudulent ice company funding scheme to open up New York voting to non-property owners. By the 19th century Democrats were legalizing immigrants right off the boat with two witnesses on hand to swear to the status of every newly arrived immigrant, even if he didn't speak English.
The problem was that most of those immigrants tended to get jobs, produce a second generation, move on and become socially or politically conservative. Unions provided a temporary stopgap for Democrats trying to hold on to the working class vote but Reagan beat them there. Race and religion proved to be somewhat more enduring methods of plantation politics, but in the end those were far too feeble bases. To perpetuate the Democratic vote, perpetual immigration was and is required. New immigrants feed the Democratic party which is based around catering to the supposedly disenfranchised. Of course that requires disenfranchised people which requires constant immigration.
In Europe, liberal parties discovered the same thing late in the 20th century, that the flow of immigrants who were there as cheap labor if given the vote, would be certain to vote for them. These parties were forced to make the same transition that the American liberal Tammany Hall party machine had made when it went from keeping the Irish out to inviting them in, once it was clear that harnessing immigrants meant a seat of power for liberal politicians.
One might imagine that conservatives would see things otherwise, but that is too naive. Conservatism is the flip side of liberalism, conservative movements often require some progressive movement to be reactionary toward, just as some clergymen need violent movies and pornography to denounce, many conservative politicians need immigration to create a constant flow of change in order to secure their own place with a traditional constituency.
Consider Tancredo's endorsement of Romney, a candidate best known for campaigning on immigration endorsing a candidate with nearly no immigration credibility whatsoever. But what a politician appears to value is not what he always really values.
Politicians are often lawyers and often think the way lawyers do. To remain in demand, you need a problem that appeals to a certain segment of the public, which also requires that the problem continue being a problem. If divorce ended, divorce lawyers would be out of business. If murder rates dropped, what would criminal defense attorneys do. There are plenty of conservative politicians that campaign against immigration but would not remotely want the problem to go away.
Beyond them of course, American conservatives have come to represent free enterprise, which in its distorted sense places the interests of corporations above the interest of the nation or the public. And corporations want cheap labor above all else. Big businesses in the 19th century in the supposedly anti-slavery North were willing to embrace slavery to keep the international trade going. Those same businesses promoted the importation of immigrants in order to feed the machine of Industrial slavery that took in 7 year olds and spat out disfigured and blinded 9 year olds. Not as much has changed as people like to think. Politicians face a business climate in which businesses demand that either a blind eye is turned to their illegal labor practices or they'll move on to Mexico or China. And so the blind eye gets turned regardless of who is in office because in the end politicians protect the jobs and businesses in their district and every politician has such businesses to protect.
Finally both liberal and conservative politicians are dedicated to government spending, which requires an expanding tax base which requires an expanding population of workers. With birth rates dropping across the West, that expanding population can only come from immigration. Neither liberal nor conservative politicians are genuinely committed to cutting entitlements or cutting pork or cutting budgets and to keep the flow of spending going, more workers must be taxed, more corporations must be appeased with cheap labor and the great river of immigration must continue.