The Senate may have passed a comprehensive immigration-reform bill after months of labor, but the legislative battle is just beginning. House Speaker John Boehner has announced that he’ll only bring a bill to the floor if it enjoys the support of a majority of House Republicans (a standard practice). The Republicans of the Senate’s bipartisan Gang of Eight have so failed to impress their colleagues in the House that the lower chamber won’t even use their bill as a starting point. They’ve got a lot of writing to do.

Republican criticism of the Senate bill has focused on several problems. The most fundamental flaw is that its structure will swiftly break the political coalition needed to pass and enforce it. Those who primarily support the bill because they want to legalize the illegal population get what they want quickly, as the bill grants a form of legal status when some minimalist security targets are met; those who primarily support the bill because of its enforcement and border-security provisions will have to wait longer to get what they want, and in the event of any hiccups they’ll be unable to appeal to their old coalition partners for support. Obviously, this elementary flaw will have to be addressed.

The second line of attack has focused on some rather nebulous metrics for border security, so the House bill surely will include a stronger position here. Yet tougher border enforcement won’t solve the illegal-immigration problem any more than tougher drug enforcement has solved the drug problem. Illegal immigration, like the drug trade, is driven by demand. As long as large numbers of employers are willing to hire illegal immigrants, there will be large numbers of illegal immigrants. Breaking that relationship must be the centerpiece of any serious reform.

And the Senate bill makes a serious attempt at that by requiring employers to vet the legal status of their new hires with a system known as E-Verify. Contrary to popular imagination, most illegal-immigrant employment in the United States isn’t completely off the books—about three-quarters of illegal immigrants simply use a fake Social Security number. E-Verify allows employers to check whether the Social Security numbers their employees provide are genuine. In theory, then, it would be very difficult for illegal immigrants to support themselves in the United States, prompting them to leave. In practice, the bill leaves a bit to be desired. It makes E-Verify mandatory over a period of years, years that special interests might use to weaken it. It also doesn’t require current employees to be run through the system—only new ones. And some Republicans have expressed concerns that stronger forms of E-Verify, such as one that includes photographs, could form the backbone of a national ID system—a tool the government could easily abuse. So the House bill will likely adjust the upper chamber’s E-Verify language.

One way to assuage concerns about E-Verify’s effectiveness without laying the foundations of a national ID would be to backstop it by verifying legal status with other techniques. And the government already has the infrastructure in place to do this, as William W. Chip explained in last month’s American Conservative:

Employers are already obligated to submit a Form W-4 to the IRS that gives the name and social security number of every new employee. The IRS shares that information with the Social Security Administration (SSA), which knows which numbers are invalid—or are suspicious because there are being used in multiple locations or belong to children or the very elderly—and generally does nothing about it. The SSA refuses to share evidence of fraudulent use of Social Security numbers with U.S. Immigration and Customs Enforcement (ICE). When Bush administration officials approached the chairmen of the Social Security committees in Congress about a fix, they were rebuffed.

In other words, but for a handful of senators and congressmen jealous of their bureaucratic prerogatives, the federal government would not need to mandate E-Verify. If employers knew that ICE would be notified of false or suspicious Social Security numbers—“G-Verify”—unscrupulous employers would be deterred from hiring workers they knew to be illegal, and most honest employers would voluntarily enroll in E-Verify to avoid the hassle.

Using “G-Verify” (i.e., government verification) to support E-Verify has crucial advantages over using either independently. G-Verify alone would create lots of work for the government, so using it in tandem with E-Verify is a must. A second point of enforcement would reduce the need to add risky extras like photos to E-Verify. G-Verify would drive employers toward E-Verify, as Chip says. E-Verify allows employers to determine a new hire’s status faster and with less government involvement than G-Verify, while G-Verify would still work if the Senate bill’s protection of current employees from E-Verify stands. A two-pronged system would be harder to avoid and harder for opponents to dismantle. And by making it harder for illegal immigrants to find work, it would remove a key incentive for illegal immigration—increasing the chance that America's second immigration reform to end all immigration reforms will be the last.