The House voted Friday to cancel the annual diversity visa lottery and give those immigration visas to high-tech foreign-born who earn advanced degrees from American universities, as Republicans powered through their chamber the first major immigration bill since the election.

The 245-139 vote was a test of the GOP’s plan to tackle immigration piecemeal, and while the bill passed, the strong opposition from Democrats suggests that Republicans’ strategy will face difficult hurdles.

And while the chief selling point of the bill was to boost green cards given to science, technology, engineering and technology students, the bigger fight came over Republicans’ plans to cancel the diversity visa lottery, which the GOP argues is rife with fraud.

“We want to put to the head of the line the people who, every single one of them that comes, net creates jobs,” said Rep. Darrell Issa, California Republican, who managed the bill on the House floor.

Democrats, though, objected to making immigration a zero-sum equation, where any new visas would have to come at the expense of existing lines of immigration.

“I can’t support a bill that pits immigrant communities against each other,” said Rep. Zoe Lofgren, the ranking Democrat on the House immigration subcommittee.

She also said that it’s not a one-to-one exchange, and immigration would actually decrease under the GOP bill.

While all 55,000 diversity visas are used every year, she said statistics from the National Science Foundation show that there are only about 30,000 students a year who would even qualify.

After Hispanics were credited with helping boost President Obama in this year’s elections, both parties have been eager to find ways to tackle immigration.

Democrats say they want to pass a broad bill that legalizes most illegal immigrants and rewrites the legal immigration system, while House Speaker John A. Boehner has said his chamber will go piece-by-piece.

Both Republicans and Democrats agree more should be done to keep desirable would-be immigrants, such as those earning advanced degrees, here in the U.S. But they disagree over whether to do that as a stand-alone, or what should be coupled with it.

In the case of this week’s bill, it eliminates the diversity visa lottery — a long-time target of some Republicans, who say it invites fraud and could be a national security risk.

The lottery doles out immigration visas based on chance, with the goal of giving those in lesser-represented countries a chance to earn a spot. Every year, millions of would-be immigrants apply for the 55,000 slots.

House Judiciary Committee Chairman Lamar Smith, who wrote the legislation, said the visa lottery invites fraud.

In an effort to sweeten the bill for Democrats, he included a provision that would allow legal immigrants to let their family members, who are also seeking green cards, to wait in the U.S. with them, rather than have to wait in their home countries.