WASHINGTON — In the weeks that led to the huge across-the-board cuts to federal spending early this year, Obama administration officials warned of dire consequences for the Justice Department: F.B.I. agents dropped from investigations, United States marshals pulled from their beats, federal prison guards furloughed.

Then when the cuts known as sequestration hit, the Justice Department suddenly found more than half a billion dollars in unspent money from the previous year. Furloughs were called off. The Boston Marathon bombing investigation proceeded unhindered. In short, there were few of the predicted calamities, although several antipoverty and science programs like Head Start and the National Institutes of Health suffered damage.

But while the most dire predictions may not have materialized in 2013, the tricks that many agencies employed — deferring maintenance, using unspent money from earlier years, cutting staff by attrition — are likely to be exhausted by 2014, when federal departments must trim an additional $24 billion from already tight budgets.

House and Senate budget negotiators, forced together by the deal that ended the recent 16-day government shutdown, will finally sit down on Wednesday to devise a spending plan for the current fiscal year. Though Republicans and Democrats remain far apart on virtually every matter of policy, they agree on one: sequestration must end.