The provision has emerged as a point of contention among Republicans, who criticize it as an example of wasteful spending that would neither create jobs nor otherwise improve the economy.
Under the provision, states no longer would be required to obtain federal permission to offer family planning services - including contraceptives - under Medicaid, the health program for the low-income.
Democrats considered the politically-potent change as congressional budget experts estimated it would take slightly longer for the overall legislation to achieve an impact on the economy than the administration projects.
The Congressional Budget Office said the economy would feel the effects of almost two-thirds of the money over the next year and a half. The administration claims 75 percent of the funding would be absorbed in that period of time, and Obama has pledged that the bill he signs will meet that target and either save or create up to 4 million jobs.
While the debate surrounding the overall impact of the measure pits economists and their statistics against one another, Republicans quickly seized on the family planning money as evidence that the Democrats were advancing an agenda that went beyond the economy.
"How you can spend hundreds of millions of dollars on contraceptives how does that stimulate the economy?" House Republican Leader John Boehner, R-Ohio said on Friday after congressional leaders met with Obama at the White House. "You can go through a whole host of issues that have nothing to do with growing jobs in America and helping people keep their jobs."
Several Democrats said Monday night that Obama had spoken personally with Rep. Henry Waxman, D-Calif., about removing the provision. Waxman is chairman of the committee with jurisdiction over Medicaid and a close ally of Speaker Nancy Pelosi, D-Calif.
The Democrats who described the likely reversal did so on condition of anonymity, saying they were not authorized to disclose developments not yet made public.
Obama's request to House Democrats underscores the administration's desire to signal a spirit of bipartisanship, a recurring theme for the president in his first week in office.
Whether it also succeeds in gaining votes is unclear, particularly in the House, where the GOP leadership has advanced an alternative that consists almost exclusively of tax cuts. The only new spending in the Republican plan is to maintain the current system of up to 33 weeks in unemployment benefits for several additional months.
By contrast, the White House-backed bill includes about $550 billion in spending and $250 billion in tax cuts.
Much of the funding in the Democratic bill is ticketed for health care and education, as well as money to weatherize buildings and build highways and other transportation projects.
A companion measure is making its way to the Senate floor for a vote next week, and congressional leaders have pledged to have legislation ready for Obama to sign by mid-February.
White House Budget chief Peter Orszag said in an AP interview that he's confident that the more ambitious target can be met for getting money into circulation in the economy, especially with changes likely to be made in the bill before it reaches the White House.
"With appropriate attention and proper management, you can both get the money out the door ... and still have well-selected projects," Orszag said.
"I don't see how that's possible," said Sen. Thad Cochran of Mississippi, top Republican on the Senate Appropriations Committee. "They'll be just pouring money down on the ground if they achieve that goal."