Senate Majority Leader Mitch McConnell set up a Wednesday vote.
Republicans need 60 votes to move forward with the bill.
Senators are trying to tackle the two issues before leaving Washington.
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.