WASHINGTON — After months of unrelieved gloom and discord, Congress and President Barack Obama are starting to make a dent in the federal budget deficit. It’s projected to shrink slightly to $1.28 trillion this year, and bigger savings from this month’s debt ceiling deal are forecast over the next decade.

No one’s celebrating. There will be plenty of red ink for years to come.

The nonpartisan Congressional Budget Office projected Wednesday that annual budget deficits will be reduced by a total of $3.3 trillion over the next decade, largely because of the deficit reduction package passed by Congress earlier this month. The office also forecast persistently high unemployment, a troubling political prospect for President Barack Obama in the crucial months of his campaign to win a second term.

Even with the anticipated big savings, annual budget deficits are expected to total nearly $3.5 trillion over the next decade — and much more if Bush-era tax cuts scheduled to expire at the end of next year are extended. In all, nearly $8.5 trillion would be added to the national debt over the next 10 years if the tax cuts and certain spending programs are kept in place, the budget office report said. The national debt now stands at more than $14.6 trillion.

The numbers help illustrate the urgency facing a new joint committee in Congress that is charged with finding $1.2 trillion to $1.5 trillion in budget savings over the next decade.

Most of the improvement in this year’s deficit picture comes from higher than anticipated tax collections from 2010 returns filed in the spring. Over the longer term, the belt-tightening required in the new deficit reduction law will mean even bigger savings, the report says.

Deficits could end up larger if CBO’s economic forecast, which is more optimistic than private projections, proves to be too rosy. The agency doesn’t foresee another recession but modest economic growth over the next few years. And it expects the unemployment rate to fall only slightly, to 8.5 percent in the last three months of 2012, and staying above 8 percent through the following year.

“A great deal of the pain of this economic downturn still lies ahead of us,” said CBO Director Douglas W. Elmendorf.

At $1.28 trillion, this year’s budget deficit would be the third highest, surpassed only by those of the past two years.