Sen. John McCain's family said Monday that the senator is responding well to continued cancer treatment and hopes he will return to work in Washington, D.C., by January.

"Senator McCain has returned to Arizona and will undergo physical therapy and rehabilitation at Mayo Clinic. He is grateful for the excellent care he continues to receive, and appreciates the outpouring of support from people all over the country. He looks forward to returning to Washington in January," his family said in a statement Monday morning.

One of McCain's doctors in Washington reported on Monday that his recent viral infection is being successfully treated.

"Senator McCain has responded well to treatment he received at Walter Reed Medical Center for a viral infection and continues to improve. An evaluation of his underlying cancer shows he is responding positively to ongoing treatment," Dr. Mark Gilbert, chief of Neuro-Oncology at the National Institutes of Health's National Cancer Institute, said in a statement released Monday.

McCain will miss this week's historic vote on the GOP tax bill.