McGrath said Barbara Bush continues to be treated for her bronchitis with antibiotics, and she said she feels "a thousand percent better today."
He said President Bush 41 is also on the upswing. He is alert and remains in stable condition in intensive care, and he said the good news he is being actively evaluated for having his breathing tube removed.
"He is doing better -- of course he has a ways to go -- but it's hard not to be encouraged," McGrath said Thursday night.
McGrath said both had a great night's sleep.
Their son Neil Bush has been over to visit. No other family members are flying in because they feel everything is stable and moving in the right direction.
Former President George W. Bush is still going to the inauguration, McGrath said.
The 92-year-old former President was admitted to the intensive care unit at Houston Methodist Hospital to address "an acute respiratory problem stemming from pneumonia. Doctors performed a procedure to protect and clear his airway that required sedation," McGrath said in an earlier statement.
By Wednesday evening, the former President was no longer sedated.
McGrath told CNN doctors wanted to keep George H.W. Bush in ICU for observation, because he's still intubated and their intention is to keep his airway open.
At first, McGrath reported that he was responding well to the drugs. But Wednesday, the 41st President's condition changed and he was admitted to the intensive care unit, sedated and intubated.
"It's definitely very concerning," said Dr. Sanjay Gupta, CNN's chief medical correspondent, who noted that it is the first time President Bush has been intubated to protect his airway. "Certainly when someone is sedated, they're having trouble breathing on their own."
Barbara Bush treated with antibiotics
Barbara Bush also was admitted to the hospital Wednesday morning as a precaution after "experiencing fatigue and coughing," McGrath said in the same initial statement.
McGrath said Wednesday evening the first lady has bronchitis, not pneumonia like her husband.
Bush, who served a single term as President from 1989 to 1993, was already not expected to attend the inauguration of President-elect Donald Trump in Washington on Friday due to health concerns.
Bush sent a letter to the President-elect on January 10, apologizing for missing the ceremony and saying that he and Barbara "wish you the very best as you begin this incredible journey of leading our great country."
"My doctor says if I sit outside in January, it likely will put me six feet under. Same for Barbara," Bush wrote, in a letter first reported by ABC News. "So I guess we're stuck in Texas."
Trump responded on Twitter Wednesday, wishing the Bushes a speedy recovery and thanking them for their note.
"Looking forward to a speedy recovery for George and Barbara Bush, both hospitalized. Thank you for your wonderful letter!" he tweeted.
President Barack Obama said at a White House news conference Wednesday his White House has been in touch with the Bush family.
"They have not only dedicated their lives to this country, they have been a constant source of friendship and support and good counsel" over the years, Obama said.
"They are as fine a couple as we know," he added, calling the Bushes "really good people."
Former President Bill Clinton, also offered his best wishes to his predecessor on Twitter.
"41 and Barbara—thinking about you both and sending wishes for a speedy recovery. Love, 42," he wrote.
The 41st president has, in fact, heard from all of the former presidents, along with Obama and Trump's teams.
President Bush also received a "get well" video from actress Suzanne Somers and his face lit up, McGrath said.
Previous health concerns
Bush revealed several years ago that he suffered from a form of Parkinson's disease that left him unable to walk. He uses a wheelchair or a scooter to get around and had two other health scares in 2014 and 2015.
In December 2014, he was hospitalized after experiencing shortness of breath, and the following July fell at his home in Kennebunkport, Maine, breaking the C2 vertebrae in his neck.
The injury did not result in any neurological problems, his spokesman said at the time.
CORRECTION: This story has been updated to accurately state the years George H.W. Bush served as president of the United States.