The talks over spending cuts have narrowed in focus to mostly cover a relatively small corner of the budget — what is known as discretionary spending. That spending is split into two parts. One is money for the military, which the Congressional Budget Office estimates will total $792 billion for the current fiscal year. The other half funds a wide range of domestic programs, like Head Start preschool and college Pell Grants, and federal agencies like the Interior and Energy Departments. It will total $919 billion this year, the budget office estimates.

A separate category known as mandatory spending has largely been deemed off limits in the talks. That spending, which is the primary driver of future spending growth, includes programs like Social Security and Medicare.

Administration officials have proposed freezing both halves of discretionary spending for next year. That would amount to a budget cut, compared with projected spending, under the way the budget office accounts for spending levels. Spending for both parts of the discretionary budget would be allowed to grow at just 1 percent for the 2025 fiscal year. That could also amount to a budget cut since 1 percent would almost certainly be less than the rate of inflation. That proposal would save about $1 trillion over the span of a decade, compared with current budget office forecasts.

Republicans rejected that plan at the bargaining table. They are pushing to cut nondefense spending in nominal terms — meaning, spend fewer dollars on it next year than the government spent this year. They also want to allow military spending to continue to grow.

“It just sends a bad message and Republicans feel like it would not be in our best interest to cut spending at this juncture, when you’re looking at China and Russia and a lot of instability around the world,” said Representative Robert B. Aderholt, Republican of Alabama, who sits on an Appropriations panel that oversees Pentagon spending. “That’s been the basic position that most Republicans have.”