Both parties support the idea of making green cards available to students who earn advanced degrees in science, technology, engineering and math, the so-called STEM degrees, from U.S. universities. But they disagree on how to do it.

A leading point of contention was the Republican bill's repurposing of 55,000 visas issued through the visa diversity lottery to create STEM visas. Many Democrats opposed eliminating the visa lottery.

Smith needed at least 50 Democrats to support his bill to win passage. "Unfortunately, Democrats today voted to send the best and brightest foreign graduates back home to work for our global competitors," he said in a statement.

"Democrats voted against a bill that helps American businesses hire the most qualified foreign graduates with advanced STEM degrees," said Smith. "Their vote against this bill is a vote against economic growth and job creation."

U.S. Rep. Zoe Lofgren (D-Calif.), who introduced , said she could not support Smith's bill.