Senators passed the Terri Schiavo bill on Sunday amid growing political pressure to save the woman's life.
"The president believes that this is a case where serious questions and significant doubts have been raised," White House spokesman Scott McClellan said aboard Air Force One carrying President George Bush back to Washington, where he is expected to sign the bill when it is ready.
"That's why he believes we ought to have a presumption in favour of life," the spokesman added.
Forty-one-year-old Terri Schiavo has been in a persistent vegetative state for the past 15 years, following a cardiac arrest that damaged her brain.
Her feeding tube was removed on Friday, after a protracted legal battle that pits the woman's husband, Michael Schiavo, against her parents, Bob and Mary Schindler.
Michael Schiavo insists Terri should be allowed to die because that was her wish communicated to him when she was well.
"The president believes that this is a case where serious questions and significant doubts have been raised. That's why he believes we ought to have a presumption in favour of life"
White House spokesman
The Schindlers argue their daughter should be kept alive and have questioned Michael's fitness to serve as his wife's guardian.
A Florida state judge, believing Michael Schiavo's testimony about his wife's wishes, had ordered her caregivers to stop feeding her.
But under the bill passed by the Senate, a federal district judge will receive jurisdiction over the case, thus setting the stage for a new protracted round of litigation.
The House of Representatives, meeting in a special session on Sunday, was expected to convene at 0200 GMT on Monday to hold a three-hour debate before voting on the measure, which will then be sent to Bush for his signature.
"The bill has overwhelming bipartisan support in the House," House Republican Majority Leader Tom DeLay said, adding that he had no doubt it would pass easily.
But House Republicans failed to move the measure as fast as they had hoped because Democrats objected to rushing it through without debate.
That forced the House leadership to spend time ensuring a quorum by bringing members, who had already left for their districts for the Easter holiday, back to Washington.