@Eorl,
Well, i don't know what exactly you mean by viable. Do you mean plausible? I'd say not necessarily, as there have been right-wing, even reactionary political movements (and existant forces preserving the status quo, such as the Holy Alliance) in Europe without reference to immigration. In the United States, there have been strong themes both of reactionary and "nativist" (i.e., anti-immigration) movements, such as the Know Nothings, as well as very liberal movements which have demanded the guarantee or expansion of civil rights, such as the Grange. In Canada, the CCF (Cooperative Commonwealth Federation) was created by welding together labor movement organizations with farmers organizations. Although the Tories were eventually able to torpedo the CCF by associating them in the minds of people with communism, it was reborn as the NDP (New Democratic Party), which has formed several provincial governments, and which is now the Official Opposition in the national government. That is despite a deep and persistent thread of "Toryism" and plutocracy in Canadian history.
I see your point, but either anti-immigrant sentiment (all this in my never humble opinion) will simply "envigorate" existing reactionary movements--that is to say, poison their rhetoric further; or it will spawn new political movements. The good news is that, in the United States at least, anti-immigrant movements had never had much in the way of "legs." The Know Nothings (as they were called--they called themselves various names, such as the Native American Party or the American Party) never attracted effective leaders, and their one trick pony never gave them even the status of spoilers or power-brokers. The slavery issue destroyed the party, such as it was, and that had only ever been a sometimes successful party in local politics. It was chiefly obsessed with the Irish and the Germans--most of the German immigrants of the 1840s and -50s had come from southern Germany, especially after the failed 1848 socialist uprisings, which meant they were Catholic. The Irish, of course, we automatically seen as Catholics, even when they happened to be Ulster Protestants, who never came in large numbers. So the Know Nothings were essentially a WASP movement. Their lack of appeal not only condemned them to a lack of effective leadership, but prevented them from becoming a force nationally. They were limited to the areas where immigrants were highly visible--Boston, New York, Philadelphia and, to a lesser extent cities on the Great Lakes (immigrants arriving in Boston or New York would travel north via the Erie Canal and then west across the Lakes).
Today's obsession with illegal immigrants is strongest in the border states of the southwest, although it does show up elsewhere. Of course, the Latin American immigrants come over the border there in large numbers. But there is some conservative anti-immigrant sentiment elsewhere in the country, because Latin Americans have become ubiquitous. (They are usually called "Mexicans" wherever they are found, but that's only because the hating class are too stupid to know or care that they come from many nations.)
In the 1840s and -50s, the Know Nothings never attracted strong, charismatic leadership for a very simple reason--they were swimming against the tide. All the "Lilly White" (i.e., white supremecist, Protestant) sentiment, all the instances of "No Irish Need Apply" were meaningless in the face of the prospect of cheap, uncomplaining labor. It was only late in the 19th century that the Irish and the Germans got involved in labor organizing movements--previously, they had been a source of cheap, compliant labor.
The same thing now applies to Latin Ameican immigration. Many of them take jobs which Americans have little interest in. When i lived in Ohio, Latin Americans had pretty well taken over the fast food labor market. High school kids turned their noses up at $10/hour jobs at MacDonalds or Burger King, while Latin Americans not only snapped up those jobs, but were soon well entrenched in the lower level management of fast food outlets. Whether legal or illegal, many employers have quite an interest in the Latin American labor force, so the reactionaries can fulminate to their hearts' content--nothing of real substance is going to come out of Congress about the issue, and the anti-immigrant movement will have no legs as long as people with money (and therefore political power and influence) find the labor force immigrants provide to be useful.
Although i cannot profess as detailed a knowledge of anti-immigrant movements in Europe, from what i can see, economics trump xenophobia and racism there, too.