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 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 return 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 would leave debt at $27.6 trillion at the end of the decade, according to the Congressional Budget Office.