“The cuts Republicans propose would have severe impacts on education, public safety, child care, veterans’ health care and more,” the White House budget director, Shalanda Young, wrote in a memo last week.

Republicans have for months cited growing federal spending and debt as the reason they have refused to raise the nation’s borrowing limit — risking default — unless Mr. Biden agrees to spending cuts.

Representative Garret Graves of Louisiana, one of Mr. McCarthy’s top negotiators, said this week that the biggest gap with Biden administration officials was on spending numbers. “My interpretation of their position is that they fail to recognize or fail to see to the fact that we are on a spending trajectory right now that is absolutely unsustainable,” he said.

Federal spending spiked during the Covid-19 pandemic, first under President Donald J. Trump and continuing under Mr. Biden, as lawmakers delivered trillions of dollars in assistance to businesses, people and state and local governments. It remains higher than historical norms, when measured as a share of the economy, which is the easiest way to track spending patterns as prices have increased over time.

The Congressional Budget Office estimates that total spending averaged just under 21 percent of gross domestic product from 1980 through 2019, just before the pandemic hit. It surged above 30 percent in 2020 and 2021. This fiscal year, it is expected to be just over 24 percent, falling slightly over the next several years and then beginning to grow again in the waning years of this decade, climbing past 25 percent in 2033.

Discretionary spending, though, is expected to decline over the decade as a share of the economy. Military spending — which Republicans have thus far refused to reduce as part of talks with Mr. Biden’s team — should tick down slightly from 3 percent of the economy. Discretionary spending outside the military is now 3.6 percent but is expected to fall to 3.2 percent by 2033.

Social Security and Medicare, conversely, are expected to grow rapidly over the next 10 years, as retiring baby boomers qualify to receive health and retirement benefits. Social Security spending will rise from 4.8 percent to 6 percent of the economy in that time, the budget office projects, and Medicare will rise from 3.9 percent to 5.3 percent.