Sen. Tim Johnson, D-S.D., was in critical condition Saturday and resting from brain surgery.
"At this point, no news is good news," spokesman Noah Pinegar said.
Johnson had a brain hemorrhage Wednesday, weeks before Democrats are to take over the Senate with a one-vote majority.
His condition has appeared to improve since the surgery. Johnson has responded to voices, opened his eyes and moved his limbs.
Johnson, 59, had emergency surgery late Wednesday after being rushed to the hospital from his office. The surgery relieved pressure on the brain and stopped the bleeding.
Surgeons said in a statement Friday that the senator was experiencing post-surgery swelling in his brain, but they said that was normal.
Johnson's doctors also disclosed that when he arrived at the hospital, Johnson felt weakness on his right side. That condition probably will require physical therapy as part of his recovery.
He has been diagnosed with arteriovenous malformation, a condition that causes arteries and veins to grow abnormally large, become tangled and sometimes burst. The condition often is present from birth.
South Dakota Gov. Mike Rounds, a Republican, would appoint a replacement if Johnson were to leave office. A Republican appointee would create a 50-50 tie and effectively allow the GOP to retain Senate control because of Vice President Dick Cheney's tie-breaking vote.
There is ample precedent for senators to continue to hold office while incapacitated. Unless Johnson's seat is vacated by his death or resignation, Democrats would retain the majority.