WASHINGTON—The Trump administration has drafted preliminary economic growth forecasts in its federal budget planning that rely on assumptions that are far rosier than projections made by independent agencies and most private forecasters, according to several people familiar with the discussions.

The forecasts are being revised, these people said, following an internal debate. One concern is that pressing staff economists to produce aggressive forecasts might undercut the credibility of top appointees forced to later defend those numbers.

The deliberations show the challenge the administration faces as it tries to reconcile the competing goals of cutting taxes, boosting military and infrastructure spending, preserving Medicare and Social Security programs and keeping budget deficits from soaring.

Economic growth forecasts are presented as part of White House budget submissions to Congress and are due out from the Trump team in the coming weeks. They have an important impact on projected debts and deficits. A fast-growing economy produces more revenue while reducing the need for spending on programs such as food stamps or unemployment insurance. Fast growth estimates can thus hold down projected deficits.

The forecasts, which were initiated before President Donald Trump took office, project gross domestic product—a broad measure of national output of goods and services—growing between 3% and 3.5% a year over the coming decade, with inflation-adjusted annual growth ultimately settling at around 3.2% during the later years of the 10-year forecast.

The economy has grown around 2% on average over the past decade. Many economists believe sustained growth at more than 3% will be difficult to achieve without a sharp rebound in productivity growth and a reversal in the slowing expansion of the U.S. labor force, developments few are projecting. Worker productivity growth has slowed to 0.7% a year since 2010, a sharp slowdown from rates exceeding 3% in the late 1990s and early 2000s.

The internal Trump projections are at odds with other assessments of the economy’s long-run growth prospects. The Congressional Budget Office, a nonpartisan agency that provides analysis to Congress, estimates the economy will grow 1.9% annually between 2021 and 2027. The Federal Reserve forecasts growth of 1.8% over the long run. While there are often disparities between the White House and other agencies on growth projections, they are rarely this large.

“The president ran a campaign on proposals that would be incredibly pro-growth,” said Lindsay Walters, a White House spokeswoman. “There is a process in place where the administration develops an economic forecast based on its policies that are included in the president’s budget. That budget is still being finalized.”

During the campaign, Mr. Trump made apparent his low regard for economists. His administration has yet to name any of the three members to his Council of Economic Advisers, which oversees forecasting and other modeling.

The forecasts were prepared by Trump transition officials who met with officials at the Treasury Department and the CEA after the election, according to five people familiar with those discussions.

“It is awfully hard to get to 3%. I don’t know where a number like that would come from,” said Dale Jorgenson, a Harvard economics professor who specializes in such projections. Mr. Jorgenson’s most recent forecasts show an economy growing by 1.8% annually over the next decade. That’s in part because the labor force is aging, meaning there are fewer workers to produce goods and services, and because the educational attainment of the workforce has plateaued, meaning workforce skills aren’t advancing. Major policy changes such as a tax-code overhaul could boost growth to 2.4%, he said.

Trump officials believe a regulatory rollback and a tax-code revamp will unleash growth that drives a recovery in productivity, sends business investment higher and draws idled workers back to the labor force. They also assume interest rates would remain low because the U.S. would become a more attractive place to park money.

The higher annual growth estimates in the initial internal Trump forecasts would result in the U.S. economy becoming 17% larger after a decade relative to recent projections from the CBO, which produces forecasts that assume no changes to current tax and spending policies.

The higher growth assumption in the Trump forecast would show sharply lower deficits as a share of gross domestic product, especially in the back half of the 10-year forecast window.

Maya MacGuineas, president of the Committee for a Responsible Federal Budget, a group that advocates deficit reduction, said Mr. Trump’s policies to boost spending on the military and to cut taxes are likely to increase deficits.

“The risk is that rosy economic scenarios allow us to borrow trillions of additional dollars in the next couple of years, doing real damage” if growth doesn’t materialize, she said.

Republicans in Congress won’t be able to rely on such estimates when they produce a budget resolution for the coming fiscal year because they use estimates from the CBO.

Boosting growth faces other challenges. It is possible the Fed would move faster to raise interest rates in order to prevent the economy from overheating if growth began to accelerate and stirred inflation. The Fed has raised short-term rates twice since 2015 and plans more moves in the months ahead.

The internal growth projections struck some people who saw them as extraordinarily optimistic because they assumed inflation would remain low and interest rates wouldn’t increase much beyond policy makers’ current expectations despite the big growth spurt.

Mr. Trump campaigned on some policies that could raise other hurdles to growth, particularly limiting immigration. Net immigration currently accounts for nearly all of the growth of the working-age population, an important underpinning of economic growth. “If you slow the immigration rates a bit, it’s going to cost you in terms of growth,” said Mr. Jorgenson.

What’s unusual about the administration’s forecasts isn’t just their relative optimism but also the process by which they were derived. Normally, the executive branch starts with a baseline forecast prepared by career staff of the CEA.

Officials then calculate how their policy changes add or subtract to that forecast. Those exercises are managed by the so-called troika—top political appointees at the CEA, the Treasury Department and the White House budget office. The heads of each department make final signoffs.

Discussions for the Trump administration unfolded differently, with transition officials telling the CEA staff the growth targets that their budget would produce and asking them to backfill other estimates off those figures.

These projections could shift as top personnel at key agencies take their jobs. The Senate confirmed Steven Mnuchin as Treasury secretary on Monday and Mick Mulvaney as White House budget director on Thursday.

“The biggest thing I’m surprised about is they don’t have the people in place to do this,” said Douglas Holtz-Eakin, who served as an economist in both Bush administrations before leading the CBO. “No one is at the CEA, so how is this getting done?”

All presidents put a positive spin on the growth effects of their policies, allowing them to project higher growth than independent forecasts. In January 2016, for example, the CBO said the economy would grow 2% annually between 2021 and 2025. The Obama administration said a few weeks later that if all of its proposed policies were adopted, GDP would rise 2.3% over the same period.

One person involved in several previous budget processes said he had never seen career staff asked to make such aggressive assumptions about economic growth as during the new administration. Several people involved in past budget deliberations said those discussions have usually centered on whether growth would be one or two-tenths of a percentage point higher than other estimates, not a full percentage point.

Republicans and Democrats in prior administrations said presidents have typically been hesitant to produce implausibly glowing projections because it could weaken their credibility with Congress and the public.

“A fair amount of time and energy is spent making sure the forecast is internally consistent,” said Mr. Holtz-Eakin.