Republican pushback on immigration deal grows more extreme - The Washington Post

House Majority Leader Steve Scalise (R-La.) invoked the 5,000 number late Sunday while saying flatly that the House won't vote on the deal. He claimed it "accepts 5,000 illegal immigrants a day." 

This is false. That's merely the point at which a very restrictive process kicks in (it would also kick in if crossings reach 8,500 in a single day). At that point, no new asylum claims from those apprehended would be considered, and anybody caught crossing the border would be removed...

https://www.washingtonpost.com/politics/2024/02/05/gops-false-amnesty-claims-give-away-game/