2 Senate Republican John Thune told reporters that Johnson's plan has "a lot" of support among Republicans in the Senate, adding: "It'd be strong."
The Republican-controlled House passed HR-2 in May, but the bill has gone nowhere in the Democratic-led Senate.
Among other things, the Senate Republican proposal would resume construction of a border wall -- former President Donald Trump's signature goal -- in addition to deeming large numbers of migrants ineligible for asylum.
Republican border provisions face broad opposition from Democrats in Congress and from President Joe Biden.
He told reporters that a bill linking Ukraine aid to border security would come soon.
Persons:
San Nicolas de los, Daniel Becerril, Mike Johnson, Republican John Thune, Lindsey Graham, Tom Cotton, James Lankford, Donald Trump's, Joe Biden, Johnson, David Morgan, Scott Malone, Deepa Babington
Organizations:
REUTERS, Rights, U.S, Senate Republicans, Republican, Republicans, Democratic, Democrats, Internal Revenue Service, Thomson
Locations:
U.S, Nuevo Leon, San Nicolas, San Nicolas de los Garza, Mexico, Ukraine, Republican, Israel