TRENTON — The Department of Transportation has told New Jersey that if it pays back all it owes, it will be credited nearly half the $271 million it owes the federal government for a scrapped New York-New Jersey rail tunnel.

New Jersey got the tunnel tab for money already spent after Gov. Chris Christie abandoned the $8.7 billion project because of potential cost overruns. The payment is due on Dec. 24.

Transportation Secretary Ray LaHood signed a Dec. 14 letter confirming that $128 million would be credited to a congestion-mitigation account after New Jersey repays the debt.