Despite White House opposition, the House appears likely to pass a bill this week that would allow more foreign students who graduate from U.S. schools with advanced technical degrees to stay in the country.

The House failed to pass the bill, drafted by Judiciary Committee Chairman Lamar Smith, R-Texas, when it was brought to the floor in September under a procedure that requires a two-thirds vote to pass. But based on the vote from that first attempt, the legislation appears to have enough support to pass the chamber this week by a majority vote.

The bill would eliminate the Diversity Visa Program and shift up to 55,000 green cards a year to foreign students who graduate from qualified U.S. schools with a doctorate or master’s degree in the “STEM” disciplines: science, technology, engineering, and math.

Smith’s STEM bill is slated to come up for debate on Thursday. Smith did make some minor changes to the measure, including making it easier for family members of STEM green-card holders to stay in the United States while they wait for their own green cards, and allowing unused STEM green cards made available in fiscal years 2013 through 2016 to be used in the future. The original bill would have only allowed for unused STEM green cards that were available in the first two years covered by the bill to be rolled over into future years.

Still, even supporters acknowledge that the bill faces long odds in the Senate, where Democratic leaders on the issue, such as Sen. Chuck Schumer, D-N.Y., favor including STEM green-card legislation as part of broader immigration reform.

Schumer introduced his own STEM green-card bill in September.

On Wednesday, the White House issued a statement of administration policy opposing passage of the House bill for several reasons, including that it “would allocate immigrant visas for advanced graduates of a limited set of STEM degree programs.” The statement said the Obama administration is “deeply committed” to immigration reform but “does not support narrowly tailored proposals that do not meet the president’s long-term objectives with respect to comprehensive immigration reform.”

Tech firms and lawmakers argue that immigrants have been responsible for helping to start some of the most successful tech firms in the United States, including Google and Yahoo, and that it makes no sense to educate foreign students in the key STEM fields and then force them to leave the United States when they graduate.

Both Democrats and Republicans support the goal of allowing more skilled foreign students who graduate with advanced STEM degrees to remain in the country, but Smith’s bill faces continued resistance from key House Democrats, including Rep. Zoe Lofgren, D-Calif., who has offered her own STEM green-card legislation. She has criticized the bill for eliminating the Diversity Visa Program. The program uses a lottery to allocate up to 55,000 green cards to people from countries with low rates of immigration to the United States.

“Republicans know they have an anti-immigrant image problem, yet, unfortunately, they are proceeding with the Smith bill to pretend they’re pro-immigrant, even though it is a divisive bill that actually reduces legal immigration,” Lofgren, the top Democrat on the House Judiciary Immigration Subcommittee, said in a statement on Tuesday.

“Republicans need to move past these kinds of gimmicks and work with Democrats to reform our immigration system so it works for businesses, our economy, and families,” Lofgren said. “I am ready to work seriously with Republicans on top-to-bottom reform and hope that real progress can be made early next year.”

Critics of the Diversity Visa Program, however, argue that it has been prone to fraud. The State Department even posted a warning on its website advising people to be wary of scams related to the program. “The Diversity Visa invites fraud and absolutely means that we would have a security risk if we were to continue it,” Smith said during the House floor debate on his bill in September.

However, some tech-industry officials and other groups say they welcome action on the issue.

“Passing this bill into law will greatly benefit the United States, because STEM graduates will be able to innovate and create companies here that have the potential to employ thousands of Americans,” Keith Grzelak, vice president for government relations for the engineers group IEEE-USA, said in a statement.

Grzelak’s group released a report on Tuesday that argued the Diversity Visa Program has achieved its goal and is no longer needed.

“The data shows that the visa lottery has made itself unnecessary, and even counterproductive, which is clear from comparing the educational level and potential contribution to the American economy of STEM graduates from the same regions and countries,” the report concluded.

This article appeared in the Thursday, November 29, 2012 edition of National Journal Daily.