Immigration reform is one of President Barack Obama's priorities for his second term, and for a wide-reaching package to pass, lawmakers need to be convinced that the border with Mexico is secure.
But that is no easy sell.
Apprehensions of undocumented aliens at the frontier have dropped 50 percent since 2008, going to 365,000 people last year, which the Obama administration cites as evidence that border security measures work.
And deportations of aliens without residency permits, particularly those with criminal records -- a key government goal -- stand at about 400,000 a year.
But the investigative arm of Congress, the Government Accountability Office (GAO), dampened the government's optimism last week.
A report submitted to the House of Representatives said the number of apprehensions at the US-Mexico border "provides some useful information but does not position the department to be able to report on how effective its efforts are at securing the border."
"The Border Patrol is in the process of developing goals and measures; however, it has not yet set target timeframes and milestones for completing its efforts," it added.
Marc Rosenblum, an immigration policy expert with the Congressional Research Service, said that "the size and diversity of the US border mean that no single, quantitative, off-the-shelf indicator accurately and reliably provides a metric or a 'score' for border enforcement."
Another report found that southern US cities, in particular El Paso, Texas just across the border from drug violence-plagued Ciudad Juarez, are the safest in the country, with constantly dropping rates of all kinds of crime. That study was based on FBI figures.
So far, the Republicans, who control the House, have been adamant that they will not approve major immigration reform until they are convinced the border is secure.
US authorities estimate there are 11.5 million illegal aliens in the United States, most of them Mexican and Central American, though the flow from Mexico has practically dried up.
Homeland Security Secretary Janet Napolitano says a 100 percent secure border is impossible, and now she has to deal with her slice of the so-called sequester, or deep cuts in public spending.
It means her funding will be slashed by an amount equivalent to the salaries of 5,000 border agents.
The border between the United States and Mexico is the busiest in the world, with 350 million people crossing it every year.
Figures on border activity have always been problematic because they only take into account apprehensions and people caught more than once trying to sneak in, not those who do make it across into the US, or the effect of factors such as like tunnels.
Three years ago the Department of Homeland Security announced it would use a new measuring tool, called operational control of the border, with five levels of effectiveness.
When the agency acknowledged that it had top- and second-level control of only 57 percent of the more than 3,000 miles (4,800 kilometers) that make up the border with Mexico, Republicans expressed outrage.
The department dumped that tool the next year, and for now it uses figures on apprehensions of illegals.
The GAO report said Homeland Security has pledged to present new goals and timeframes in November of this year -- a target that hardly suits the White House's stated goal of getting reform passed in a matter of months.
One idea being debated is to create an independent commission that will determine when it thinks the border is secure.
Advocates of immigration reform that the debate could really go on forever.
"You're never going to seal that border," Napolitano said in a speech last week.
But another key factor in the debate is this: around 40 percent of the illegal aliens in the country probably entered the United States legally, with a visa that has since expired, according to Homeland Security figures.