WASHINGTON — Facing a Friday deadline, the Senate is on track to shore up federal highway aid and veterans’ health care, leaving a raft of unresolved issues for a jam-packed congressional agenda in the fall.

The Senate plans to take up a House-passed bill on Thursday that would extend spending authority for transportation programs through Oct. 29 and replenish the federal Highway Trust Fund with $8 billion. That’s enough money to keep highway and transit aid flowing to states through mid-December.

Authority for the Transportation Department to process aid payments to states is slated to expire at midnight Friday.

Just before leaving for its August recess on Wednesday, the House overwhelmingly approved the three-month extension on a vote of 385-34.

Lawmakers said they were loath to take up yet another short-term transportation funding extension — this will be the 34th extension since 2009. But Republicans and Democrats don’t want to see transportation aid cut off, and they are eager to pass an amendment to the extension bill that fills a $3.4 billion hole in the Department of Veterans Affairs’ budget. The money gap threatens to force the closure of hospitals and clinics nationwide.