AFRUSTRATED PRESIDENT Obama complained the other day that Republicans in Congress have been moving the goal posts on border security, demanding ever more unachievable levels of enforcement before they would consent to fixing the nation’s immigration system. Next, Mr. Obama joked, the GOP would demand a moat across the U.S.-Mexican frontier — with alligators.

That line got a good laugh. In fact, Republican posturing on border security is deadly serious, and worse than the president suggested. Even in the face of overwhelming evidence that the border has become safer and less leaky, the GOP would have the nation believe the opposite.

Using such scare tactics, Republicans are trying to distort the debate on immigration and justify their opposition to reform.

Exhibit A for Republican distortion is Rep. Lamar Smith (Tex.), chairman of the House Judiciary Committee, who recently assigned a “failing grade” to U.S. Customs and Border Patrol efforts along the Mexican border. Mr. Smith based his “failing grade” on the fact that the Border Patrol classifies just 44 percent of the nearly 2,000-mile border as being under “operational control.” That sounds bad, until you ask what it actually means. The answer: not much.

A case in point is the Marfa sector, a 510-mile stretch of desolate terrain in southwestern Texas comprising more than a quarter of the frontier between the United States and Mexico. According to the Border Patrol, just 10 percent of the Marfa sector is under “operational control,” meaning agents can reliably stop crossers at or near the border.

But it also happens that the Marfa sector, owing to its isolation, sparse population and forbidding, deep river canyons, is the least crossed, sleepiest area of the entire southwest border. The Border Patrol arrests scarcely a dozen people a day along the entire length of the sector, despite (or because of) the 700 agents assigned there, triple the 2005 number.

Adding hundreds more agents, as Republicans imply is necessary, would be a massive waste of money — and still wouldn’t guarantee “operational control,” owing to the region’s rugged topography and inaccessibility. Homeland Security Secretary Janet Napolitano, like her Bush administration predecessors, agrees that total operational control is an unreachable goal. As Border Patrol officials will tell you, Marfa and other lightly trafficked segments of the southwestern frontier are the least of their problems and represent no particular threat to America’s security.

The fact is that the United States has established tighter control of the border than at any time in recent memory. Serious crime is down dramatically in almost every major American town along the frontier. As Rep. Silvestre Reyes, an El Paso Democrat, pointed out, the six largest southwestern border cities have lower crime rates — and, specifically, lower rates of murder, rape, robbery and burglary — than the six largest cities in Ohio, home state of Republican House Speaker John A. Boehner, whose spokesman said last week that immigration reform was dead until violence at the border was checked.

Thanks largely to President Bush, the Border Patrol has almost doubled its strength along the Mexican frontier since 2004. The 17,700 agents there now — supplemented by drones, fencing, sensors and other technology — are a formidable force. Other federal agencies and personnel, including thousands of agents and analysts with Immigration and Customs Enforcement and the Drug Enforcement Administration, plus 1,200 National Guardsmen ordered to the border by Mr. Obama last year, contribute to an increasingly muscular presence. Tighter border security, combined with America’s economic travails, has contributed to a dramatic drop in illegal border crossings, reflected in the fact that apprehensions along the border have been cut in half over the past five or six years. The Border Patrol arrested fewer illegal crossers along the entire frontier in the fiscal year that ended last July (448,000) than it apprehended in the Tucson area alone in 2004 (492,000).

The border is not impenetrable; few land boundaries are. But no number of boots on the ground, and no amount of fence-building, will choke off the flow of illegal immigrants entirely as long as employers demand their services in the United States. Of the 11 million undocumented immigrants in this country, an estimated 7 million hold jobs, despite the spike in unemployment of the past few years.

Mr. Smith’s strategy, and that of many Republicans, is to whittle away at the problem through enforcement, not only at the border but in the workplace as well. A growing movement among Republicans would also deny citizenship to the U.S.-born children of undocumented immigrants. By making pariahs of the undocumented millions, and by attrition, they believe America can eventually rid itself of most illegal immigrants.

That strategy is a fantasy and a recipe for ongoing failure. Too many powerful interests — not least, businesses that form a critical part of the GOP coalition — will oppose it.  And the economic reality is that American-born workers, increasingly well educated, are unwilling to take the low-skill jobs that many immigrants fill in landscaping, hospitality, poultry processing and other industries. Eleven million undocumented immigrants won’t fade away from American communities and the labor force. The dilemma of illegal immigration will remain unresolved until Republicans enter into a dialogue based on facts, not fear.