WASHINGTON — At an impromptu news conference this week, Senator Joe Manchin III, Democrat of West Virginia, lamented the “shell games” and “budget gimmicks” he said his party was using to artificially reduce the $1.85 trillion price tag of the spending bill moving through Congress, saying the real cost was probably double that amount.

“This is a recipe for economic crisis,” Mr. Manchin warned, suggesting that he would not support a bill without understanding its potential impact on the economy.

Four years ago, as Republicans marched ahead with a $1.5 trillion tax cut, top Democrats in Congress assailed them for hiding the true cost of the legislation, arguing that it was “loaded with budget gimmicks” and packed with “stealthy tax tricks” that would saddle the nation with even more debt. Now, as they race to finish their own trillion-dollar domestic policy package, Democrats are employing their own maneuvers to downplay the cost of their bill.

President Biden’s new framework for tackling climate change, bolstering child care and a wide range of other economic programs assumes that the package will be fully paid for with an estimated $2 trillion in tax increases on corporations and high earners.

But budget experts, along with some moderate Democrats, say the true cost of the legislation will be closer to $4 trillion because of the way the programs are structured and accounted for in the budgetary process. For instance, many of the provisions in Mr. Biden’s framework would expire, or “sunset” after only few years, even though Democrats anticipate that they would eventually be extended.

The assumption that spending on those programs will cease in a few years reduces their overall cost during the 10-year budget window that Congress uses to determine whether a bill will add to the federal deficit. That is especially important given the way in which Democrats are trying to pass this particular bill. Lawmakers have limited room for adding to the deficit over a 10-year period because of the budget procedure known as reconciliation that will allow them to pass the legislation without Republican votes.

The nonpartisan Congressional Budget Office will eventually provide a formal “score” of cost of the final legislation before it passes, and some lawmakers have begun demanding that tally before they will commit to a vote. On Thursday, the Joint Committee on Taxation released a report projecting that the tax increases in a bill the House is preparing to vote on would raise $1.5 trillion over a decade.

The Center for a Responsible Federal Budget, a fiscal watchdog group, suggested that the true cost of the legislation Democrats are crafting could be around $4 trillion given the number of expiring programs.

That includes an increased child tax credit and an expanded earned income tax credit that would last for just a year, expanded Affordable Care Act premium tax credits that would last for four years and universal pre-K, which would last for six years.

“It’s similar but it’s much more egregious,” said Marc Goldwein, senior policy director for the Committee for a Responsible Federal Budget, comparing the situation to 2017. “They’re cutting the bill in half, more than in half, by having things expire early.”

A proposal this week by some House Democrats to temporarily suspend a $10,000 cap on the amount of state and local taxes that households can deduct through 2025 and then reinstate the limit in 2026 highlighted the use of budget gimmicks. Such a plan would have a negligible impact on the 10-year deficit window since the revenue lost over the next five years would be recouped beginning in 2026. But Democrats from high-tax states have said they want the cap repealed entirely, and there is a chance that it would never return after the reprieve.

Kent Smetters, the faculty director of The Penn Wharton Budget Model, said the proposal had echoes of the temporary tax cuts that Republicans passed for individuals in 2017. Those cuts are set to expire in 2025 but are expected to be extended because allowing them to sunset would result in a politically unpalatable tax increase on low- and middle-income earners.

“You try to get something through on the personal side and hope that a future Congress will take it up and extend it,” Mr. Smetters, whose team has been advising Mr. Manchin on some budget concerns, said in reference to the tax code.

Some Democrats have also looked skeptically on that proposal. Senator Robert Menendez, a New Jersey Democrat who has been pushing for permanent relief from the cap on the state and local tax deduction, known as SALT, said this week that it should be targeted to benefit the middle class but not reinstated. Such “gimmicks,” he warned, would mostly benefit the rich.

On Wednesday, House Democrats unveiled a bill that included a measure to raise the SALT cap to $72,500 through 2031. The Joint Committee on Taxation projected that this would actually raise $2 billion in additional tax revenue over a decade.

In some cases, Democrats and the White House are making much rosier assumptions about the revenue that the bill will bring in, through its policies and projected economic growth.

For instance, the Biden administration has called for spending $80 billion to bolster the enforcement staff at the Internal Revenue Service and estimated that would raise $400 billion in additional revenue over the next 10 years by giving the agency greater capacity to catch tax cheats.

Other analysts, such as those at the Congressional Budget Office, projected it would raise far less — about $200 billion over a decade. The discrepancy boils down to a difference of opinion about the value of the “deterrent effects” of having more tax agents conducting audits.

The overall impact of the proposed legislation on the economy is not certain. The Biden administration said last week that its plan would spur economic growth. The Treasury Department said on Thursday that the legislation would “generate net deficit reduction” by raising taxes on big companies and wealthy Americans.

However, the Penn Wharton Budget Model released on Thursday found the overall cost of the House Democrats’ bill is not fully covered by tax increases and said it would be a slight drag on economic growth in the long term.

The use of budget gimmicks is a longstanding Washington tradition that has been employed by both parties.

As Republicans were crafting their tax cut bill four years ago, they were not shy about using gimmicks to whittle down the cost. Lawmakers tinkered with delaying the corporate tax cut, they set individual tax cuts to expire in 2025 and they phased out other tax breaks that intended to give an initial boost to business investment.

The Bush tax cuts that passed in 2001 and 2003 were originally scheduled to expire in 2010, for budgetary reasons, but they were extended during the Obama administration and some were ultimately made permanent.

That has not stopped conservative groups and Republican lawmakers from seizing on the sleight of hand to criticize Democrats. A group of top Senate Republicans called on Democrats to allow for a rigorous accounting of the legislation before casting votes.

“Hiding the details of the real cost of the trillions of dollars in new government spending and tax increases by using budgetary gimmicks is an attempt to disguise the true cost and impact the reckless tax and spending spree will have on the nearly $29 trillion national debt, rising prices, jobs and inflation,” they wrote.