The Senate will vote on a both a six-year bill and a short-term extension.
The House is expected to leave Washington Wednesday for the August recess.
The Senate's highway bill overcame another procedural hurdle on Monday.
Senators could vote Monday on attaching the Export-Import Bank to the highway bill.
The clock is ticking to renew highway funding before lawmakers leave for the August recess.
The House bill comes in the wake of a San Francisco shooting that launched a political firestorm.
A vote in the Senate hasn't been scheduled, but Republicans suggested they could try again on the highway bill.
The Senate will plow through its highway bill despite the House passing its own version.
The Senate will continue its work on an overhaul of the Bush-era No Child Left Behind law.
The Senate is expected to finish its work on the education bill this week.