IN THE VENOMOUS debate over illegal immigration, there is a point of agreement between President Obama and some of his would-be Republican rivals, including former Massachusetts governor Mitt Romney. They’d like to see undocumented immigrants “get to the back of the line” for citizenship. Unfortunately, that convergence of views distorts rather than illuminates the debate.

Granted, Mr. Obama and Mr. Romney have different ideas of how the “line” would work. The president doesn’t seem inclined to force unauthorized immigrants to leave the country before applying for legal status. Mr. Romney thinks it would be nice if they somehow “self deported,” then lined up back home for legal re-entry to America. In the end, the distinction is meaningless — because there is no line, not even a relevant visa category, for millions of immigrants.

Here’s why. A large majority of the 11 million illegal immigrants are unskilled or low-skilled Mexicans. Many of them have no relatives over age 18 who are either U.S. citizens or permanent residents in possession of green cards.

That makes them ineligible for any realistic visa category. They are barred in most cases from employment-based visas, which favor skilled and well-educated applicants, and from family-based visas, which require applicants to have spouses, parents or siblings who are U.S. citizens or hold green cards. (Even the “line” for those visas often takes 15 to 20 years or more.) There is simply no immigrant visa category for which most unskilled Mexicans qualify and no realistic prospect they could be legally admitted to the United States. About half of the unauthorized adults in the country are Mexicans who probably have no category for admission, according to Pew Hispanic Center senior demographer Jeffrey S. Passel.

However, there will continue to be a demand for their labor. At least 7 million illegal immigrants are in the American work force, in many cases doing jobs most Americans consider too dirty or unsuited to their educational attainment. (A half-century ago, about half of American men dropped out of high school to seek unskilled work; today just 10 percent do.)

There is a tiny number of “other worker” immigrant visas for which Mexicans may apply. But those applications take several years and require employer sponsorship. And no employer would go through the time and expense of sponsorship for an unskilled worker.

It is possible to argue that the United States should shift away from family-based visa preferences toward employment-based ones or that it should create a new category of visas for skilled or unskilled “fortune seekers,” who, like millions before them, want to come to America because of its record of rewarding hard work and hustle.

Likewise, we would like to see an improved guest worker program, one that offered American employers some reasonable prospect of filling jobs with adequate numbers of immigrant employees in a timely way. But as things stand now, those things don’t exist.

On the campaign trail, it may sound tough or fair or common-sensical to demand that illegal immigrants “get to the back of the line.” In fact, it is a convenient fiction, a trope designed more to obfuscate than resolve a policy mess that politicians find too hard to tackle.