McCain, who was diagnosed with brain cancer earlier this year, was admitted to a Maryland hospital on Wednesday and treated for several days for side effects from chemotherapy.
In a statement, the 81-year-old lawmaker said he would undergo rehabilitation and physical therapy there after being hospitalized at Walter Reed Medical Center, near Washington.
"Senator McCain has responded well to treatment he received at Walter Reed Medical Center for a viral infection and continues to improve".
"Senator McCain is now receiving treatment at Walter Reed Medical Center for normal side effects of his ongoing cancer therapy". A doctor says he is also "responding positively" to ongoing treatment for brain cancer.
McCain's absence will leave Republicans with the simple majority (51 votes) needed to pass the tax reform bill under the chamber's reconciliation rules.
McCain will not attend the GOP's tax bill vote which is expected to take place sometime early this week.
"I did speak to Cindy McCain, and I wished her well, I wished John well".
"They've headed back, but I understand he'll come if we ever needed his help, which hopefully we won't", Trump said.
"He's going through a very tough time, there's no question about that", Trump said. "But he will come back if we need his vote".
McCain's daughter, Meghan tweeted he was doing well and the family will spend Christmas together in Arizona.
Last week, Republican Sens.
A vote is expected in the House and Senate on Tuesday. Marco Rubio (R-FL) and Bob Corker (R-TN) announced their support for the bill after winning some amendments or provisions.
Republicans secured the support of Florida Sen.
But McCain's condition has appeared to worsen in recent weeks.
McCain is unlikely to return to Washington this year, one of the sources said.
More recently, McCain tore the Achilles tendon on his right foot, which forced him to wear a walking brace and then use a wheelchair in order to get around the U.S. Capitol.