WASHINGTON -- Former Vice President Dick Cheney is headed to Capitol Hill to offer congressional Republicans some budgeting advice.

Cheney is scheduled to meet Tuesday evening with top House GOP leaders to warn against Pentagon cuts, scheduled for January, that Congress agreed to in last summer’s debt deal with the White House. Cheney also met behind closed doors with Senate Republicans at their weekly luncheon.

The visit comes as Republicans are making an orchestrated effort to attack Obama on defense issues, an area where the GOP and its national security hawks have traditionally dominated Democrats in public opinion.

Attitudes may be shifting, though, as Americans have turned against military actions in other lands and appear to prefer spending on American shores. Polls also show they support the White House proposal to tax wealthier Americans as a way to help balance budgets.

The dispute stems from the requirement in the budget deal for a round of automatic cuts, beginning in January, across the federal budget after Congress and the president failed to agree to a deficit reduction plan.

Top Pentagon brass have warned the defense cuts scheduled for the new year – “sequester” in budget-speak – would decimate the military. The summer debt deal also included commensurate cuts to non-defense programs – but Republicans now want to spare the Pentagon to make deeper cuts to food stamps and other domestic programs.

“As former vice president and Secretary of Defense, he has a keen understanding of the threat posed by the president’s Defense sequester,” said a senior GOP aide who declined to speak on the record in order to discuss the private meeting. “We look forward to getting his insight.”

The White House quickly suggested it was “odd” that House Republicans would be taking budget advice “from somebody who famously declared that deficits don’t matter” – a reminder of a Cheney commentary during the George W. Bush administration, as the nation’s debt load doubled.

“The president obviously has a different view, which is that deficits do matter,” Deputy Press Secretary Josh Earnest told reporters traveling with Obama to events in Texas, “which is why the president has laid out a balanced approach to deal with out long-term deficit challenges. He’s hopeful that we’ll finally get Republicans to agree to work with him on that effort.”

Congressional Democrats have said they are unwilling to undo last summer’s debt deal unless Republicans drop their opposition to a higher tax rate for the wealthy.

Obama and his Hill allies have proposed allowing the Bush-era tax rates for incomes for families making beyond $250,000 a year to expire in December, as scheduled, and some Democrats have suggested the new revenue could be used to offset the cuts coming to the Pentagon.

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Lisa.mascaro@latimes.com

Twitter: @lisamascaroindc