Two painful rounds of cost-cutting on Capitol Hill and higher-than-expected tax collections will push this year’s budget deficit down by $300 billion and slice nearly $1.5 trillion from deficits over the next decade, according to new White House projections.

But the report says that the national debt, which stands at $14.6 trillion, would still continue to climb if a budget proposed by President Obama in February were enacted. The debt would rise to $24 trillion by 2021 — or 99 percent of the nation’s entire annual economic output.

White House budget director Jacob J. Lew said that the report, released Thursday, “underscores that we need to get back on a sustainable fiscal path and that we need to invest in economic growth and job creation.”

While lawmakers approved significant spending cuts in the recent battle over the federal debt limit, Lew said, the new budget projections make clear that the Budget Control Act of 2011 “didn’t finish the job.”

The summer budget update, known as the “mid-session review,” predicts that this year’s deficit will be just over $1.3 trillion. The forecast was based on economic projections through the end of June. Since then, the economy has deteriorated markedly, prompting administration officials to take the unusual step of offering an alternative forecast updated through August.

Under the new scenario, budget deficits would be slightly higher over the next decade, the report said. And the unemployment rate would fall far more slowly, hovering around 9 percent through the 2012 presidential election — an ominous sign for Obama.

The report comes as Obama prepares to address Congress next week on the nation’s twin economic challenges. Even as Republicans press for additional spending cuts to tame federal borrowing, Democrats are clamoring for more government spending to create jobs and kick-start economic growth, which could in turn improve the long-term budget picture.

Obama has pledged to address both issues in September, starting with a speech to Congress next Thursday laying out a new strategy for creating jobs. The White House has already called for extending emergency unemployment benefits and a payroll tax holiday for workers. Administration officials also are considering tax breaks to reward employers for hiring and fresh spending on construction projects, job training and housing.

Lew declined to provide details, but said the jobs proposal would “be designed to be both effective and something we can work on a bipartisan basis to get enacted into law.”

To avoid driving deficits higher, administration officials have said Obama also intends to lay out a detailed plan to cover the cost of those initiatives — likely to exceed $200 billion over the next decade — and to further reduce future borrowing.

Using his recent deficit-reduction talks with House Speaker John A. Boehner (R-Ohio) as a template, administration officials have said that Obama would lay out a framework for restraining borrowing that calls on a new congressional debt panel to aim much higher than the $1.5 trillion savings target it was given this summer.

Republicans have been dismissive of those efforts, and argued that Thursday’s report provides further evidence that Obama’s economic policies are not working.

In a statement, House Budget Committee Chairman Paul Ryan (R-Wis.) noted that the new report indicates the unemployment rate will remain above 8 percent throughout Obama’s first term in office — a level administration officials said in 2009 could be avoided by enacting an expensive economic stimulus package.

“Today’s report confirms that the president’s policies have failed to deliver on his promises of job creation, deficit reduction and much-needed economic growth,” Ryan said. “Since taking office, the president’s policies have made a difficult situation worse.”