"Millions of Americans are watching right now," the president told reporters in a brief news conference in the White House Rose Garden. "Their families and businesses are counting on us. After all, this is why they sent us here: to finally confront the challenges that Washington had been putting off for decades. To make their lives better. To leave this country stronger than we found it."
Obama's comments came shortly after he had returned to the White House from Capitol Hill, where he met with the House Democratic leadership.
The president said he reminded lawmakers "that opportunities like this come around maybe once in a generation. Most public servants pass through their entire careers without a chance to make as important a difference in the lives of their constituents and the life of this country.
"This is their moment, this is our moment, to live up to the trust that the American people have placed in us - even when it's hard; especially when it's hard. This is our moment to deliver.
"I urge members of Congress to rise to this moment. Answer the call of history, and vote yes for health insurance reform for America," Obama said.
Lawmakers emerging from that meeting appeared confident that their health care legislation would pass the vote scheduled for Saturday evening.
"Today we will make not only history, but progress for America's working families," Speaker Nancy Pelosi told reporters assembled outside the meeting room.
"We're on the cusp of making an historical decision on behalf of the American people," added House Majority Whip James Clyburn of South Carolina.
A senior Democratic aide quoted the president as saying during the meeting that he was "absolutely confident that you guys will get this done."
"Absolutely confident that when I sign this in the Rose Garden, each and every one of you will be able to look back and say 'this was my finest moment in politics,'" the aide quoted Obama as saying.
White House spokesman Bill Burton said the president made the case that Congress has a historic opportunity today to provide stability and security for those who have insurance, affordable coverage for those who don't and bring down the cost of health care for families, small businesses and the government.
Burton also reported that Obama told the Democratic lawmakers that they had made more progress on comprehensive reform than any administration and any Congress in the past 70 years, and that they should take this historic opportunity to pass health care reform so that he can sign a bill by the end of this year.
"Now is the time to finish the job," the president said in the Rose Garden. "The bill that the House has produced will provide stability and security for Americans who have insurance; quality, affordable options for those who don't; and lower costs for American families and American businesses."
The Democratic leadership meeting with the president took place as debate on the nearly $1.1 trillion bill began in a special Saturday session in the House.
Later in the day, anti-abortion Democrats will introduce an amendment to the measure that would ban most abortion coverage from the public option and other insurance providers in the new so-called "exchange" the legislation would create, three Democratic sources told CNN.
The prohibition would exclude cases of rape, incest or if the mother's life is in danger.
Several anti-abortion Democrats will offer the amendment, including Rep. Brad Ellsworth, D-Indiana, and Rep. Bart Stupak, D-Michigan.
House Minority leader John Boehner told reporters after debate on the legislation had begun that the GOP leadership strongly supports that amendment.
"We believe taxpayer funding of abortion is wrong, and we will do everything we can to stop that from happening, by passing the Stupak amendment," he said.
The fact that the amendment will be allowed to be proposed is a big win for anti-abortion Democrats and the U.S. Conference of Catholic Bishops, which used its power - especially with conservative Democrats in swing congressional districts - to help force Democratic leaders to permit a vote that most of them oppose.
"We didn't have a choice," said a Democratic leadership source. "We didn't have the votes" on health care without agreeing to this.
Planned Parenthood decried the amendment, saying it would result in the elimination of abortion coverage currently offered by most private health insurance plans.
"This amendment would violate the spirit of health care reform, which is meant to guarantee quality, affordable health care coverage for all by creating a two-tiered system that would punish women, particularly those with low and modest incomes," the group said in a statement.
"Women won't stand for legislation that takes away their current benefits and leaves them worse off after health care reform than they are today."
The Democratic sources said people would be able to purchase riders with their own money for insurance that includes abortion coverage.
Stupak and other anti-abortion Democrats have argued for a strict abortion ban for some time.
However, Ellsworth had offered a less strict compromise measure that would have prohibited taxpayer dollars for abortions.
But Liz Farrar, a spokeswoman for Ellsworth, told CNN that some two dozen Democratic lawmakers made it clear that they needed assurances from the Catholic bishops before they could sign on - and that the religious group made clear it wanted to bolster the abortion restrictions.
As Stupak offered the amendment before the House Rules Committee overnight, several abortion rights activists on the panel argued the amendment goes too far.
"I find this amendment very, very uncomfortable," said Rep. Jim McGovern, D-Massachusetts.
"I foresee for poor women in America, a return to the dark ages," said Rep. Alcee Hastings, D-Florida.
Adding to the mix are members of the Congressional Hispanic Caucus, who staunchly oppose adding a provision to the bill that would bar undocumented workers from using their own money to buy health insurance policies available
through the exchange.
The measure is already included in the Senate Finance Committee's version of the bill, and is backed by the White House. Some conservative House Democrats have also indicated their support for the Senate language.
Several Hispanic Caucus members who discussed the issue with Pelosi Friday said they had received assurances the Senate language would not be included. Rep. Charlie Gonzalez, D-Texas, warned Thursday that several caucus members might try to block the House bill if it's changed to conform to the Senate measure.
Pelosi's bill currently includes various requirements for immigrants to verify their citizenship before getting federal subsidies to buy health insurance. Conservatives, however, have called the requirements insufficient.
Many conservatives, particularly on the Republican side of the aisle, also continued Friday to raise questions about the overall cost of the bill.
"The speaker's bill includes job-killing taxes and mandates that will hurt small businesses," Boehner said Friday. "For the sake of our families and small businesses, this job-killing bill needs to be defeated."
But some so-called Blue Dog Democrats are among those who intend to vote "no," including Rep. Stephanie Herseth Sandlin, D-South Dakota, and Rep. Frank Kratovil, D-Maryland.
"The overall cost of it is substantial," Kratovil told CNN.
The House bill would extend insurance coverage to 36 million uncovered Americans and guarantee that 96 percent of Americans have coverage, according to the non-partisan Congressional Budget Office.
Among other things, the bill would subsidize insurance for poorer Americans, establish a new government-run public option and create health insurance exchanges to make it easier for small groups and individuals to purchase coverage. It would also cap annual out-of-pocket expenses and prevent insurance companies from denying coverage for pre-existing conditions.
Pelosi's office has said the bill would cut the federal deficit by roughly $30 billion over the next decade. The measure is financed through a combination of a tax surcharge on wealthy Americans and spending constraints in Medicare and Medicaid.
The bill received a major boost Thursday when it was endorsed by AARP and the American Medical Association.
AARP, the nation's largest organization of older Americans, is a non-partisan group that advocates for people over the age of 50. The AMA, historically an opponent of health care reform, is considered one the nation's most influential doctors' advocacy groups.
Updated: 2:41 p.m.
–CNN's Dana Bash, Elaine Quijano, Lisa Desjardins, Alan Silverleib, Paul Steinhauser and Deirdre Walsh contributed to this report.