WASHINGTON — It’s all but impossible to glean from the political rhetoric, but government borrowing will grow by trillions of dollars over the next decade if the budget backed by House Republicans translates into law.

And by a few trillion more if President Barack Obama gets his way.

Call it the unpleasant truth behind a political struggle over raising the debt limit that is expected to intensify as lawmakers returned Monday from a two-week break.

While polls show voters angry over the debt, and politicians support a goal of paying it down, the two principal deficit-reduction plans would merely restrain its growth for the next decade — the Republicans’ significantly more so than the president’s.

To do otherwise, Congress “would have to enact policies that would produce a surplus,” with money left over to begin retiring debt, said Robert Bixby, executive director of the anti-deficit Concord Coalition.

The last government surplus was in 2001. For one to occur in the future would require “Republican spending policies and Democratic tax policies,” Bixby said, referring to GOP calls for deep program cuts, and Obama’s support for higher taxes. “Right now the two parties haven’t been able to agree on those kinds of changes.”

The increase in debt woven into their budgets is not a fact that Obama, Rep. Paul Ryan, R-Wis., chairman of the House Budget Committee, or any other official chooses to trumpet. The president and most lawmakers generally avoid saying directly that government debt will rise if their budget prevails — although they are careful not to claim it won’t, either. Instead, they use similar, vaguely reassuring terms.

“We have to live within our means, reduce our deficit and get back on a path that will allow us to pay down our debt,” Obama said last month as he called for $4 trillion in deficit reductions over the next dozen years. Unlike the Republicans, he favors about $1 trillion in tax increases, in addition to allowing Bush-era tax cuts on upper-income households to expire.

Administration officials say they have no estimates of the impact the president’s new proposals would have on the future size of the government’s debt, which now stands at nearly $14.3 trillion. The president’s original budget for 2012, unveiled last winter, would leave debt at $27.6 trillion at the end of the decade, according to the Congressional Budget Office. The administration itself put the figure at $26.3 trillion.

“The House Republicans’ budget reduces government spending by $6.2 trillion over the next decade and puts the budget on a path to balance in the years ahead,” Ryan wrote on the panel’s website, a theme that is similar to the one Obama struck.

Congressional Budget Office figures, however, show that if Ryan’s plan were put into law, there still would be new borrowing each year and government’s debt would total $23.1 trillion at the end of 2021. The House Republicans’ plan relies on repealing the year-old health care law, as well as deep cuts in Medicaid and domestic programs. Its most controversial provision, phasing out Medicare as it now exists, would not begin for 10 years and has no impact on debt in the current decade.

The GOP plan would generate about $4 trillion less debt than Obama’s budget envisions over the decade. Republicans point out that unlike Obama’s plan, theirs would quickly begin shrinking the debt as a percentage of the overall economy. Even so, debt would rise by nearly $9 trillion in 10 years.

The administration has asked Congress to approve borrowing beyond the current $14.3 trillion debt ceiling. In exchange, Republicans want the White House and Democrats to agree to a series of measures to cut spending in the near term and make sure it stays under control in the future. They sometimes suggest that their approach would put an end to borrowing.

“While America cannot default on its debt, we also cannot continue to borrow recklessly, dig ourselves deeper into this hole and mortgage the future of our children and grandchildren,” House Speaker John Boehner of Ohio said last winter on the day Treasury Secretary Tim Geithner notified lawmakers the limit on borrowing would have to be raised.

More recently, Rep. Jeb Hensarling of Texas, a member of the GOP leadership, said Obama “is going to have to start the process of cutting up the credit cards, pure and simple.”