The deal announced on Saturday contains smaller cuts. But the even bigger difference today is economic conditions. The unemployment rate is 3.4 percent. Prices are growing by more than 4 percent a year, well above the Fed’s target rate of 2 percent. Fed officials are trying to cool economic activity by making it more expensive to borrow money.

Michael Feroli, a JPMorgan Chase analyst, wrote this week that the right way to assess the emerging deal was in terms of “how much less work the Fed needs to do in restraining aggregate demand because fiscal belt-tightening is now doing that job.” Mr. Feroli estimated the agreement could function as the equivalent of a quarter-point increase in interest rates, in terms of helping to restrain inflation.

While the deal will only modestly affect the nation’s future deficit levels, Republicans have argued that it will help the economy by reducing the accumulation of debt. “We’re trying to bend the cost curve of the government for the American people,” Representative Patrick T. McHenry of North Carolina, one of the Republican negotiators, said this week.

Still, the spending reductions from the deal will affect nondefense discretionary programs, like Head Start preschool, and the people they serve. New work requirements could choke off food and other assistance to vulnerable Americans.

Many progressive Democrats warned this week that those effects will amount to their own sort of economic damage.

“After inflation eats its share, flat funding will result in fewer households accessing rental assistance, fewer kids in Head Start and fewer services for seniors,” said Lindsay Owens, the executive director of the liberal Groundwork Collaborative in Washington.

Catie Edmondson contributed reporting.