Sen. John McCain (R-Ariz.) leaves a closed-door session on Dec. 1 on Capitol Hill where Republican senators met to discuss overhauling the tax code. (J. Scott Applewhite/AP)

Sen. John McCain left the nation's capital Sunday to spend Christmas in Arizona with his family as he battles brain cancer, giving his Republican Party one less vote as it is expected this week to attempt to push through a contentious tax plan along party lines.

President Trump told reporters Sunday that McCain and his wife, Cindy McCain, have "headed back [to Arizona], but I understand he'll come if we ever needed his help, which hopefully we won't." He added: "But the word is John will come back if we need his vote. It's too bad. He's going through a very tough time, there's no question about it. But he will come back if we need his vote."

Trump said he spoke to Cindy McCain by phone Sunday. "I wished her well. I wish John well," he said.

McCain was hospitalized Wednesday while receiving chemotherapy treatment at Walter Reed National Military Medical Center in Bethesda and at the nearby National Institutes of Health. He received a diagnosis this year of glioblastoma, an aggressive, malignant brain tumor that can cause headaches, seizures, blurred vision and other symptoms.

In a brief statement, the senator's office provided an assessment from Mark Gilbert, chief of neuro-oncology at the National Institutes of Health's National Cancer Institute.

"Senator McCain has responded well to treatment he received at Walter Reed Medical Center for a viral infection and continues to improve," Gilbert said, according to the Associated Press. "An evaluation of his underlying cancer shows he is responding positively to ongoing treatment."

News of McCain's travel first emerged Sunday afternoon after his daughter Meghan McCain tweeted about the family's holiday plans.

"Thank you to everyone for their kind words," she wrote. "My father is doing well and we are all looking forward to spending Christmas together in Arizona. If you're feeling charitable this Christmas @HeadfortheCure or @NBTStweets to help find a cure for brain cancer is what I recommend."

McCain, 81, missed several Senate votes last week while at Walter Reed. He voted for the initial version of the tax plan, which includes sweeping tax cuts and initially passed the Senate with 51 votes. Without McCain, Republican leaders have a razor-thin margin to pass the final version, which has been in House-Senate negotiations and cannot afford any more defections.

But for Republicans, the bar to pass the legislation isn't quite as high as initially feared. Sens. Marco Rubio (R-Fla.) and Bob Corker (R-Tenn.) said last week that they will vote for the measure after indicating earlier that they would not.

McCain has been in "good spirits" while receiving treatment, Ben Domenech, Meghan McCain's husband, said in an appearance Sunday on CBS's "Face the Nation."

"I'm happy to say that he's doing well," said Domenech, a conservative writer. "The truth is that as anyone knows whose family has battled cancer or any significant disease, that oftentimes there are side effects of treatment that you have. The senator has been through a round of chemo and he was hospitalized this week at Walter Reed."

McCain, Domenech added, "remains one of the toughest men on the face of the earth, as you know."