"The president's bill will meet what has been the agreed test, that the Congressional Budget Office assesses the bill and concludes that it reduces the budget deficit. To do anything else would be irresponsible," Summers said.
But just recently, the chief actuary for Medicare and Medicaid concluded the current Senate bill would increase national health spending by about $234 billion over the next 10 years, adding a potential roadblock for fiscally-conservative Democrat or Democrat-leaning senators.
Sen. Joe Lieberman, I-Conn., said he could not vote for the bill as it stands now, and is a critic of the "medicare buy-in" proposal, which would lower the Medicare eligibility age from 65 to 55 for Americans who do not have employer-based insurance.
"It will add taxpayer costs. It will add to the deficit. It's unnecessary," said Lieberman.
On Monday the president is convening a meeting with heads of the country's largest banks, to encourage them to do more to lend to small businesses and consumers.
"President Obama is going to be talking with them about what they can do to support enhanced lending to customers across the country," Summers said. "We were there for them. And the banks need to do everything they can to be sure they're there for customers across this country."
Obama will primarily encourage the bankers to give more loans to small businesses and to allow more refinancing and restructuring of mortgages for homeowners.
For example, the president's Homeowner Affordability and Stability Plan, unveiled in February, was an attempt to benefit between 7 million and 9 million families by restructuring or refinancing their mortgages to avoid foreclosure. A White House official tells ABC News that while more than a half-million Americans signed up for the program, financial lenders have moved to refinance or restructure only 30,000 mortgages. Bankers will be told they need to do much more to make this program work.
The president will also express irritation, officials say, with the lavish bonuses these executives are paying themselves this year.
"They're still puzzled why is it that people are mad at the banks," the president told CBS's "60 Minutes." "Well, let's see. You guys are drawing down $10, $20 million bonuses after America went through the worst economic year that it's gone through in -- in decades, and you guys caused the problem. And we've got 10 percent unemployment. Why do you think people might be a little frustrated?"
The president said "there is no doubt about" the fact that the bonuses are because of the help of U.S. taxpayers. "And what's most frustrating me right now is you've got these same banks who benefited from taxpayer assistance who are fighting tooth and nail with their lobbyists up on Capitol Hill fighting against financial regulatory reform."
ABC News' Jake Tapper and Betsy Stark contributed to this report.