It was not immediately clear how long the construction pause would last.
The legislation fell well short of the 60 votes needed -- the final tally was 43 to 50 -- as nearly all Republicans voted against it.
A narrowly divided Supreme Court on Monday sided with the Biden administration in a tense dispute over the Texas-Mexico border over razor wire fencing.
The numbers are record-breaking: The Border Patrol made about 10,500 apprehensions along the southwest border on Tuesday, according to two sources familiar with the data.
There's a mix of people in encampments in Jacumba Hot Springs, California, a border town located at the U.S.-Mexico wall, and has migrants from all over the world - China, India, Turkey, and Mexico - and most don't speak English.
The Biden administration and the ACLU have reached a proposed settlement agreement that, if approved, would provide benefits for thousands of migrant families separated under the Trump administration's controversial "zero tolerance" policy to deter illegal southern border crossings.