A group of House members introduced legislation on Tuesday that would make it easier for foreign students who graduate from U.S. universities with advanced degrees in science, technology, engineering, or math to stay in the United States.

House Judiciary Chairman Lamar Smith, R-Texas, introduced the bill along with 47 House Republicans, but only one Democrat, Rep. Henry Cuellar, D-Texas, has signed on so far. The full House is expected to vote on the measure this Thursday.

The bill targets an issue both parties say needs to be addressed. Both President Obama and Republican presidential nominee Mitt Romney have voiced support for allowing foreign studnets who graduate with advanced STEM degrees from U.S. schools to stay in this country.

Supporters note that many of the most successful tech firms in the United States were created or cofounded by immigrants, including Google, Intel, and Yahoo. At the same time, tech-industry officials argue that they may be forced to move some work offshore if they are unable to keep the talent they need here in the United States.

“In a global economy, we cannot afford to educate these foreign graduates in the U.S. and then send them back home to work for our competitors,” Smith said in a statement. “For America to be to the world’s economic leader, we must have access to the world’s best talent.”

Smith’s bill would scrap the Diversity Visa Program enacted in 1990 that allows immigrants to participate in an annual lottery of up to 55,000 U.S. green cards. Instead, it would reallocate 55,000 green cards to foreign STEM graduates. It would require them to earn their degrees while living in the United States, to commit to staying in the country for at least five years, and to be sponsored by a U.S. employer. It would only apply to students who graduated from accredited U.S. colleges and universities that are at least a decade old and have been classified by the Carnegie Foundation for the Advancement of Teaching or the National Science Foundation as engaging in a “high level” of research activity.

The bill would require companies to post STEM job openings on a state workforce agency’s jobs site before seeking foreing graduates for the position. In addition, the STEM visas created by the bill would not be available to students who graduate with advanced degrees in the biological and biomedical fields.

The bill is one of many aimed at addressing the brain drain of students who come to the United States to earn valuable skills at U.S. universities but are forced to leave the country because they can’t obtain a green card or temporary work visa.

Sen. Chuck Schumer, D-N.Y., chairman of the Judiciary Immigration subcommittee, is expected to introduce his own STEM bill most likely on Wednesday that would not eliminate the Diversity Visa Program. Instead, the bill would create a two-year pilot program that would allocate 55,000 green cards a year to non-U.S. students who graduate from U.S. colleges or universities with a master’s degree or doctorate in a STEM field. His bill also would allow high-tech workers currently in the United States on temporary visas to renew their visas without having to first return to their home country.

Last week, Rep. Zoe Lofgren, D-Calif., introduced a bill similar to Schumer's measure that also would retain the Diversity Visa Program.

“We should be encouraging every brilliant and well-educated immigrant to stay here, build a business here, employ people here, and grow our economy,” Schumer said in a statement on Tuesday. “Fixing our broken green-card system will help ensure that the next eBay, the next Google, the next Intel will be started in America, not in Shanghai.”

Schumer had been negotiating with Smith on developing bipartisan legislation that could move through both chambers but they could not agree on such issues as which schools would be eligible, according to a Senate aide. Schumer’s bill is unlikely to see action before the Senate recesses this month for the November election.

Bipartisan legislation known as the Startup 2.0 Act was introduced in both chambers earlier this year that would create two new visas for foreign students who graduate with advanced STEM degrees or start businesses in the United States.

Tech firms have been supportive of these efforts but are anxious for Congress to move on the issue, which has been bogged down by the debate over comprehensive immigration reform.

“We applaud the efforts of members on both [sides] of the aisle to increase STEM visas. At present, we support the Smith bill because that’s the one that scheduled for a vote on Thursday,” Michael Petricone, senior vice president of the Consumer Electronics Association, said. “It is imperative that something get done as soon as possible — kicking out foreign-born advanced-degree holders is silly and economically self-destructive. We are hopeful that both sides can transcend politics and partisanship, and do what is clearly in the best interests of the United States.”