When Democratic House moderates raised their latest objection to voting on the party’s social spending and climate bill on Friday, they said they first needed a “score” from the Congressional Budget Office.

But those scores — detailed estimates of the fiscal and economic effects of legislation — do not always come fast.

The C.B.O. has a thankless and at times herculean job: They estimate the effects of bills on individuals, states, the economy and the federal deficit. Their scores tell lawmakers and the public what legislation will cost. They’re also a required part of the special budget process Democrats are using to pass their bill through the Senate without needing to overcome a legislative filibuster.

In the case of the Build Back Better Act — the formal name of the social spending plan — the budget office’s staff must consider a 2,000-page bill with effects throughout the economy. The bill changes tax policy; shifts the health care system; accelerates the nation’s response to climate change; and establishes new programs for subsidized child care and paid leave, to name a few of its elements. Developing detailed estimates for any of those provisions would be a big job. The budget office tries to figure out how they interact together.

“I’m sure the analysts at C.B.O are working 24-7 now,” said Doug Elmendorf, who was the office’s director from 2009 to 2015, when it scored the Dodd-Frank financial reform, the economic stimulus bill and the Affordable Care Act in rapid succession. “But their responsibility is to not make up some number and write it down, but to produce a real estimate.”

Negotiations on the package have been continuing — with final legislative details changed as late as Thursday night. Former budget office directors said such small-seeming changes can often lead to major revisions in estimates.

“These things pop up, and you’d think it’s just going to be a day or two of work,” said Keith Hall, who ran the budget office from 2015 to 2019, and is now a professor of the practice at Georgetown University. “And, no. It’s weeks and weeks of work.”

The budget office has been working alongside Congress on the legislation for months, considering various proposals and advising congressional committees on how various policy tweaks might influence the costs of different provisions. That might have led lawmakers to think a final score was just a few clicks away. But the budget office dashed those hopes Friday: According to aides, its staff told lawmakers it would not have a full estimate for the bill for a few weeks.

“Seriously, I think it’s more likely I will get calls from constituents asking what the C.B.O. is rather than asking for a C.B.O. score,” said Representative Mark Pocan, Democrat of Wisconsin, on Twitter. “Let’s go.”

Budget analysts have already assessed the costs of the bipartisan infrastructure bill, another piece of legislation that had been scheduled for a Friday vote. That bill, which the moderate Democrats support, is estimated to increase the deficit by $256 billion over the next decade.

At the time, both Senate Democrats and Republicans were quick to point to other estimates and data points that provided alternate summaries of how the bill was paid for. (“They’re kind of crazy anyway, right?” Senator Jon Tester, Democrat of Montana, said of the C.B.O.)

The demand for a score on the social spending bill caused Democrats to delay the planned Friday vote on both measures. Because Republicans are unanimously opposed to the bill, Democrats can afford to lose only three votes in the House. And Joe Manchin of West Virginia, a key centrist in the evenly divided Senate, has said he will not vote for the bill if it does not pass certain fiscal tests.

As frustrations spilled over, some Democrats warned that it was a sign that their broader agenda was in jeopardy.

“It’s obvious where this is headed,” grumbled Mike Casca, a spokesman for Senator Bernie Sanders of Vermont, the chairman of the Budget Committee, on Twitter. “House mods are going to use the C.B.O. score — no matter what it says — to vote against the B.B.B.”

The Build Back Better measure presents particular challenges. In addition to its sheer magnitude and ever-changing details, it aims to establish several brand-new federal programs, such as paid leave and child care subsidies. The office has less experience to draw upon when considering such policies than it does in assessing more familiar changes to the funding formulas for existing programs.

The constant negotiations can make that process even more difficult. In addition to its public, official scores, the office provides confidential advice to committees and leadership in Congress. In recent months, its analysts have been focused on assessing many different versions of policies. Those requests have been numerous and time-consuming for the office’s economists.

“It’s like monitoring a kindergarten class during arts and crafts,” said Zach Moller, the director of economic policy at the centrist think tank Third Way, and a former Senate Budget Committee aide. “All of the sudden, somebody spills the paste, and you’ve got to go clean that up. And while you turn your back, somebody is tugging someone else’s hair. It’s so much more complicated being the adult in the room with something like this.”

Budget office economists often must exercise judgment about questions that can be challenging to predict. Douglas Holtz-Eakin, who was the C.B.O. director from 2003 to 2005, recalled his efforts to calculate the expected costs of a terrorism insurance program in the aftermath of the 9/11 attacks. The work involved estimating the frequency and magnitude of terrorist attacks in coming years.

“You don’t want to know just how many times I just rolled dice on that one,” he said. But Mr. Holtz-Eakin, now the president of the American Action Forum, emphasized that the budget office would not serve Congress well if it cut corners or guessed about policies where it could conduct rigorous estimates.

Sometimes, the office works hard to understand the effects of a brand-new policy, and realizes later it has erred. During the debate over the Affordable Care Act, the office believed that the law’s individual mandate to obtain health insurance would have a major effect on the number of Americans who were covered under the law. In 2018, it acknowledged that years of experience had shown the provision’s impact had been substantially smaller.

Health care changes are often particularly slow to calculate. The budget office has constructed a computer model that evaluates the effects of public policy on health care insurance rates and spending. That model’s sophistication is valuable, but its heft means the program often takes a day to run, before analysts spend weeks assessing its output and interpreting the results, Mr. Hall said. He recalls explaining this process to frustrated Republican lawmakers during their efforts to repeal and replace the Affordable Care Act in 2017.

The final round of changes to the social spending package concerned price regulation for prescription drugs, a policy that could ripple through cost estimates for numerous related health programs.

When Republicans were trying to partly repeal the Affordable Care Act in 2017, the budget office faced criticisms for estimates that were politically damaging. But several C.B.O. directors said congressional angst is typically about the perceived slowness of the C.B.O. process, not the fairness of its estimates.

“I was regularly berated for not having estimates ready the instant that some legislative agreement was reached,” Mr. Elmendorf said.

The budget office is often likened to a referee in a sporting event. While referees are generally seen as neutral — and powerful — they are not always beloved figures. And particularly consequential calls tend to generate displeasure.

“They get to be the umpire,” said Rodney Whitlock, a former health policy adviser for the Senate Finance Committee, who is now a vice president at McDermott+Consulting. “Where’s the last ballgame of any kind you’ve been to where people cheer the refs?”