On Wednesday, the U.S. senator sponsoring a contentious bill to throw out per-country green card limits warned that a particular colleague might object to it when he brought it to the Senate on Thursday.

The colleague, Sen. Dick Durbin, D-Ill., did exactly that, according to a Washington, D.C. correspondent for a Kansas newspaper. That makes the third time bill S386 — also spearheaded by Sen. Kamala Harris, D-Calif. — has been blocked in the Senate this year.

The sponsor of the “Fairness for High-Skilled Immigrants Act,” Sen. Mike Lee, R-Utah, on Wednesday described the annual 7 percent cap on green cards for citizens of any one country as “a leftover from our Buddy Holly-era immigration code” and “like a vestigial organ from a bygone era.”

The annual cap has led to green card backlogs that mean waits of many years for foreign nationals seeking residency while working in the U.S. — many in the Bay Area — on the H-1B and other visas, with citizens of India, who dominate the H-1B system, waiting the longest. Lee said Wednesday in a video released by his office (around the 30-minute mark) that the 7 percent restriction advantages citizens of less-populated countries.

Under Lee’s bill S386, up to 85 percent of green cards could be allocated to Indian or Chinese citizens in 2020. In the second and third years, that proportion would rise to 90 percent.

The Center for Immigration Studies, which pushes for reduced immigration, said Thursday the bill would help Big Tech replace U.S. workers with contractors and that employment-based green cards should be issued based on merit instead of citizenship.

Lee, in the video, said he’d bring the bill to the Senate on Thursday for a unanimous consent vote that would speed it up. Last week, Sen. David Perdue, R-Ga., blocked the bill, saying he supported it but language needed to be clarified and he worried about the impact on “some specific industries.”  Lee said in the video that he’d spent the previous week “trying to iron out (Perdue’s) objections” but had just recently “found language acceptable to both sides.”

But when he brought the bill up Thursday for a unanimous consent vote, Durbin balked, according to a Kansas City Star correspondent. “Durbin told me he doesn’t support it ‘as written,’” Bryan Lowry tweeted Thursday, after tweeting that Lee’s office said the vote wouldn’t happen Thursday.

Sen. Rand Paul, R-Ky., earlier this year also blocked the bill, which was introduced in February. Lee, in the video, complained that for months he’s kept thinking he’d found “the last objector” and he described his struggle to get the bill onto the floor as “a little bit like whack-a-mole.”

A House version of the bill, HR1044, sponsored by Congresswoman Zoe Lofgren, D-San Jose, passed the House easily in July with bipartisan support.