The Senate is also expected to take up a short-term bill this week.
The Republican leader said the Senate could take up the bill next week.
The new legislation comes after GOP lawmakers huddled to hash out details of the bill.
"Please, please be angry about this," Sen. Bob Corker said.
He suggested that her refusal to take a position on the pipeline is "hard to understand."
Keith Laing 07/28/15 04:35 PM EDT
The Senate majority whip said lawmakers would negotiate a long-term fix after recess.
Jordain Carney 07/28/15 02:35 PM EDT
The House plans to leave for the August recess on Wednesday.
The senators are hoping to get the long-term bill to the House before it leaves town.
The Republican leader suggested he was proud of the Senate's long-term highway bill.
The move brings the Senate one step closer to a showdown with the House.