"We think we have found a solution" to the Terri Schiavo case, House Majority Leader Tom DeLay, R-Texas, said at a Capitol Hills news conference. "All sides agree that this is the best way to proceed."
Final approval was expected Sunday when the House planned to meet in a special session, he said.
DeLay said President Bush would sign the bill as soon as it got to him.
Schiavo's husband Michael lambasted lawmakers for getting involved.
"For Congress to come in and interfere in a personal family matter is outrageous. They can do it to me, they'll do it to every person in this country. And they should be ashamed of themselves. Leave my wife alone. Leave me alone. Take care of your own families," he said on CBS' Saturday Early Show.
Terri Schiavo's mother, on the other hand, pleaded for help from politicians Saturday as her brain-damaged daughter spent her first day without a feeding tube and protesters symbolically tried to smuggle bread and water to her.
"We laugh together, we cry together, we smile together, we talk together," Mary Schindler told reporters as supporters maintained a vigil outside the hospice where her daughter is cared for. "Please, please, please save my little girl."
Court-appointed physicians testified her brain damage was so severe that there was no hope she would ever have any cognitive abilities.
About three dozen supporters of Schiavo's parents, Bob and Mary Schindler, maintained a vigil outside the hospice where she lives. Four people, including right wing leader James Gordon "Bo" Gritz, were arrested on misdemeanor trespassing charges when they attempted to bring Schiavo bread and water, which she would be unable to consume.
"A woman is being starved to death, and I have to do something," said Brandi Swindell, 28, from Boise, Idaho. "There are just certain things that you have to do, that you have to try."
A spokesman for Schiavo's parents, Paul O'Donnell, later told reporters that they do not want supporters to engage in civil disobedience on their daughter's behalf.
"The family is asking that the protests remain peaceful," said O'Donnell, a Roman Catholic Franciscan monk.
Schiavo's parents have been attempting for years to remove Michael Schiavo as their daughter's guardian and keep in place the tube that has kept her alive for more than 15 years.
Schiavo suffered severe brain damage in 1990 when a chemical imbalance apparently brought on by an eating disorder caused her heart to stop beating for a few minutes. She can breathe on her own, but has relied on the feeding and hydration tube to keep her alive.
Republican lawmakers were rebuffed by state and federal courts Friday when they tried to halt the tube's removal by issuing subpoenas for Schiavo, her husband and caregivers to appear at congressional hearings. Gov. Jeb Bush criticized a "rush to starve her to death."
Michael Schiavo accused politicians of pandering to conservative politician groups by interfering in a personal, family matter.
"These people are pandering for votes. That's all," he said in a broadcast interview.
A White House spokesman, Jeanie Mamo, said the president, who was at his Texas ranch "was supportive of the efforts by congressional leaders. We remain in contact with Congress and the president is being kept apprised."
Saturday's legislative compromise was similar to a Senate bill passed Thursday that would let a federal court has jurisdiction in the Schiavo case. House Republicans had favored broader legislation that applied similar cases that questioned the legality of withholding food or medical treatment from people who are incapacitated.
Schiavo's feeding tube was disconnected Friday afternoon. Schiavo, 41, could linger for one to two weeks if no one intercedes and gets the tube reinserted.
Rep. James Sensenbrenner, chairman of the House Judiciary Committee, said the legislation would move the case to federal court where a judge would determine who has the legal right to decide the question of nutrition and hydration for Schiavo and whether they can be terminated.
Sensenbrenner, R-Wis., said the measure was "narrowly targeted," does not set a precedent and would allow Schiavo to resume being fed and hydrated during the legal appeals.
On Friday, Republicans used their subpoena power to demand that Schiavo be brought before a congressional hearing, with lawmakers saying that removing the tube amounted to "barbarism."
The Florida judge presiding over the case rejected the request from House lawyers to delay the tube's removal. Late Friday, the U.S. Supreme Court, without comment, denied an emergency request from the House committee that issued the subpoenas to reinsert Schiavo's feeding tube while the committee filed appeals in the lower courts to have its subpoenas recognized.