Reps. Stephanie Murphy, D-Fla., Ed Case, D-Hawaii, Josh Gottheimer, D-N.J., Kathleen Rice, D-N.Y., and Kurt Schrader, D-Ore., all refused to vote for the bill earlier this month when progressives and Pelosi wanted to advance it along with the bipartisan infrastructure bill. They cited a lack of data from the Congressional Budget Office (CBO) on how much the bill would actually cost.
But in exchange for progressive votes to pass infrastructure, the five moderates promised to vote for the reconciliation bill if the forthcoming CBO data is consistent with what the White House estimates the bill will cost.
"We commit to voting for the Build Back Better act, in its current form other than technical changes, as expeditiously as we receive fiscal information from the Congressional Budget Office -- but in no event later than the week of November 15th -- consistent with the toplines for revenues and investments" that the White House released earlier this month, the members of Congress said in a statement.
That data is expected to come Friday, setting up a possible vote to pass the bill Saturday.
The key will be whether the CBO estimates are indeed consistent with the White House's numbers – and whether the lawmakers believe the numbers on paper will reflect what the government ends up spending in reality.
There is some doubt on both of those points.
Committee for a Responsible Federal Budget (CRFB) senior vice president Marc Goldwein told FOX Business Monday the CBO numbers might say the bill will raise significantly less money than the White House estimated.
"I think the CBO numbers will be pretty similar to the White House, except for on IRS funding. Where the White House says $400 billion and I think CBO maybe will say 150," Goldwein said. "We are at 125 because we don't have a basis what will happen with some weird timing things, I could see it being a bit higher than that, but it's not going to be 400."
The CRFB puts out its own estimates for many large pieces of legislation, and it says Democrats' reconciliation bill will really cost $2.4 trillion.
Goldwein also said there are some other elements of the bill, including immigration and Medicare savings, where the CBO score may indicate it is cheaper than what the White House said. But overall, he said, "My guess is that they are a bit short of deficit neutral but probably pretty close."
In a potentially foreboding development, however, The New York Times reports the White House is preparing lawmakers for a CBO report that does not meet their expectations and arguing that the CBO is not correct in how it is calculating its score for the legislation.
Meanwhile, the CRFB released a report Monday indicating that funding tricks Democrats employed while writing the reconciliation bill obscure its true cost, which could be up to $4.9 trillion. They did this, according to Goldwein, by making some programs expire early to reduce the real dollars they cost in the bill in hopes that a future Congress will extend them or make them permanent.
"They want to spend $2.4 trillion and buy with that almost $5 trillion worth of stuff. So the way they're doing that is by making a number of the policies temporary," he said. "The problem is, once the policy's in place there is a tremendous amount of pressure to extend."
Goldwein added: "They're using 10 years of offsets to pay for, in some cases, 10 years of policy. But in some cases, six years, four years or one year of policy so they can extend them."
"We've known that for quite a while," moderate Sen. Joe Manchin, D-W.Va., said Monday when asked about funding tricks obscuring the true cost of the bill. "It's concerning. Sure, it's concerning."
Fox News asked the offices of Gottheimer, Case, Rice, Schrader and Murphy about the forthcoming CBO numbers and the CRFB report about the true cost of the bill Monday. None responded.
There are other Democrats who also are considered on-the-fence moderates on the reconciliation bill. Among them are Reps. Henry Cuellar, D-Texas, and Jared Golden, D-Maine.
That many progressives agreed to advance the infrastructure bill earlier this month with just the commitments from the five on the Gottheimer-led statement indicates they believe the math is there to pass reconciliation as long as those lawmakers are satisfied.
But the math can change quickly in the House of Representatives. And Democrats can only lose three total votes with their razor-thin majority in the House.
"We want to see what the CBO usually does, not an abbreviated one," Cuellar said Monday. "So let's see what they have. And, you know, we want to see what we're going to be voting on. So let's see what comes out by Friday."
Fox News' Caroline McKee and Kelly Phares contributed to this report.