Sen. Marco Rubio Marco Antonio RubioFlorida senators pushing to keep Daylight Savings Time during pandemic Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Intelligence chief says Congress will get some in-person election security briefings MORE (R-Fla.) is predicting that a White House-backed bill aimed at curbing legal immigration won't have enough support to pass the Senate.

"That bill's not going to pass. ... I think the White House knows that you don't have 60 votes for that in the Senate," Rubio told a Florida CBS station.

The bill, which President Trump rolled out last week with GOP Sens. David Perdue (Ga.) and Tom Cotton Tom Bryant CottonRenewed focus on Trump's Supreme Court list after Ginsburg's death Republicans call for DOJ to prosecute Netflix executives for releasing 'Cuties' Loeffler calls for hearing in wake of Netflix's 'Cuties' MORE (Ark.), would aim to move legal immigration to a "merit-based" system and cut the number of green cards given out every year.

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Trump made cracking down on immigration a key promise of his presidential campaign. But the legislation faces a steep uphill climb in the Senate, where it will need 60 votes, and is already getting pushback from several GOP senators and Democrats.

Rubio pointed to the fight over green cards as a "big difference of opinion" that he has with the White House-supported legislation, but noted he backs changes to the legal immigration system.

"Where I probably have a big difference of opinion with this bill is that it sets an arbitrary cap on the number of people that are able to come through with a green card. I don't think that should be an arbitrary cap, that number should be driven by demand," he told the Florida CBS station.

Rubio worked on the "Gang of Eight" immigration bill, which would have reformed both legal and illegal immigration.

He noted that the 2013 proposal, which passed the Senate but stalled in the House, also included a merit-based points system for legal immigration, but didn't go as far as the current proposal.

"In 2013 the very controversial Gang of Eight, four Democrats and four Republicans, proposed moving legal immigration to a merit-based system," the Florida senator said. "It wouldn't be entirely merit-based but it would be more merit-based and it has to be in the 21st century."