SPEND time listening to conservative talk radio, and the constant ranting about immigration—“Fix our broken borders, no amnesty for illegals”—might lead you to the conclusion that George Bush has no hope of ever persuading his party's base to support any plan to “legalise” America's 11m or so illegal immigrants. But you would be wrong.

According to a poll of 800 “likely” Republican voters released this week by the Manhattan Institute, the majority “believe in sensible, practical immigration reform that includes an earned legalisation process and increased border security.” The voters think there are too many immigrants, but they reject the anti-legalisation hard line of the Republican congressional leadership; and they actually seem to prefer setting the illegals on the path to full citizenship (see table).

That should give heart to President Bush and his allies on the issue, notably John McCain. However, it sits oddly with this week's blast from Michael Chertoff, the director of homeland security. He told the Senate that his policy goal “is to return every single illegal entrant, no exceptions.” He promised to show progress “in less than a year”.

The rank-and-file are showing more common sense than Mr Chertoff. It would be an economic nightmare to round up and deport all America's undocumented residents. The idea also shows little understanding of how immigration works.

As a recent report from the Pew Hispanic Centre points out, immigration—legal and illegal—is a tide that moves with the changing health of the American economy. In the first half of the 1990s, for example, the incoming flow of migrants averaged just over 1.1m a year; in the dotcom boom of the later 1990s, it rose to 1.5m a year; after the boom ended, it dropped to around 1.1m in 2002, though it has since risen to around 1.2m. The correlation is particularly noticeable with Mexican immigrants, who account for roughly a third of the overall total. In 2000, when the American economy was at its peak, some 530,000 Mexicans made the trip north; in 2002, when the American economy lost 415,000 jobs, the number of Mexican immigrants fell to 378,000.

The tide, however, never actually turns. Even in the direst times, more people come to America than leave it. In 1970, the foreign-born population of the nation was a modest 9.6m; by the 2000 census it had soared to 31.1m. Perhaps the clearest evidence of America's dysfunctional immigration system is the fact that illegal immigrants now outnumber legal ones.

Most Americans seem to think the answer is a combination of stick and carrot. Some 72% of the conservatives in the Manhattan Institute sample favoured a reform plan that would increase border security and penalise employers who hire illegal workers but would also allow illegal immigrants, on payment of a fine, to get both worker permits and the possibility of eventual citizenship. Fewer than one in five were so fixated on the stick that they would be less likely to support a politician who backed such a reform plan.

Another reason to make senior Republicans wary of immigrant-bashing is the growing prosperity of America's 41m Latinos. A new study of the Hispanic economy by Goldman Sachs points to the many advantages for companies in pursuing a young and increasingly prosperous slice of the populations: for instance, Latinos will account for a third of America's new housing in the next quarter-century. Businesses, argue the bankers, would be foolish to ignore this market. So, presumably, would political parties.