It’s unlikely, it may even be impossible, to put aside all the feelings evoked by the phrase and red flag Illegal Immigration. Wave those words around often enough, and loudly enough, and you’ll produce a debate just as confused as the one in the U.S. Senate over the filibuster – but one that’s a lot more volatile. Because this is a subject that excites the people, not just the politicians.

Each side has its own banner – “Illegal Aliens” versus “A Nation of Immigrants!” But a slogan is not an argument, no matter how often or how loudly it is repeated. Let’s try a thought experiment:

Suppose we could put aside all the distracting and provoking rhetoric about illegal immigration and come up with a common, constructive policy. What would it look like?

First, such a policy would make our borders more secure, instead of the sieve they have become. Immigration needs to be made an orderly process so that the Border Patrol can focus on looking for dangerous terrorists instead of people just seeking work. As for the millions of illegals already here, ideally we would find a way for them and their children to become recognized residents and then law-abiding citizens, instead of fugitives forever vulnerable to exploitation and discrimination.

At the same time, such a policy would need to be fair. None of these illegals should be allowed to cut in line and become eligible for legal status ahead of immigrants who have followed the rules – and have waited years before being allowed into this country. Those illegals willing to come out from the shadows would pay a hefty fine – this would be no amnesty – and become part of an open process leading to full participation in American society.

For now, these illegals are part of a vast underground economy, with all the abuses, uncertainties, and dangers that go with it. They are in effect unpersons – without the rights and protections that come with legal status. They need to be matched with willing employers, openly and legally.

A workable policy would recognize not just the illegals’ interest in becoming Americans but the country’s interest in them, for they play a crucial role in the economy. And their posterity will play a crucial role in the country’s future.

Illegal immigrants now constitute a second, hidden America, and no economy – or republic – can hope to thrive off-the-books. The alternative – just pick ’em up (by the millions) and send ’em back – makes for great demagoguery but poor policy. Besides being cruel and self-destructive (think of what mass deportations would do to the economy), adopting such a simplistic reaction to a complicated problem is unrealistic. It just ain’t gonna happen.

In short, a fair and constructive policy would look a lot like the bill just introduced by John McCain and Ted Kennedy in the U.S. Senate, and co-sponsored by Congressmen Jim Kolbe, Jeff Flake, and Luis Gutierrez in the House. Their bill in turn looks a little like the guest-worker program George W. Bush proposed last year, though it’s a decided improvement. For example, the McCain-Kennedy bill wouldn’t require these immigrants to return home after three years in order to apply for permanent residence.

Instead, it would allow them to visit family and return freely, thanks to a special new visa. And it would require three years’ residence to attain permanent residence (the coveted green card) and another three years of good behavior here to apply for citizenship.

This bill also proposes a new public-private corporation to teach immigrants English and civics, and generally prepare them to become full-fledged Americans.

No, this approach won’t eliminate illegal immigration entirely, but nothing will so long as the jobs are here and the people desperate for work are there. People will go where work is. It’s a law of economics, and maybe a law of nature. One might as well try to halt the tide.

There will always be those who, when confronted by a system that’s broken, would prefer to do almost anything besides fix it. Mainly jump up and down and generally fulminate. You can see how well that’s worked over the past decade. Playing on fear and prejudice may further the careers of politicians who know how to ride bad feelings into office, but it won’t help the country.

Too much time has been wasted thinking in terms of Them and Us. It’s time to think of how best to come together as We. Or, in the founders’ phrase, how to form a more perfect union.

Mr. Greenberg is the Pulitzer Prize-winning editorial page editor of the Arkansas Democrat-Gazette.