Republican leaders in the House and Senate told President Barack Obama they would not support delaying the start of so-called sequestration cuts next January that could slice $500 billion off planned Pentagon spending over the next decade.

House Speaker John Boehner (R-Ohio) and Majority Leader Eric Cantor (R-Va.), along with Senate Minority Leader Mitch McConnell (R-Ky.) and Minority Whip Jon Kyl (R-Ariz.), fired off a letter to Obama last Friday raising concerns about reports the Obama officials advised Senate Democratic leaders to try to delay the start of the budget cuts by six months.

“If accurate, we are troubled that rather than engaging Congress in a constructive effort to identify and enact responsible savings to replace the across-the-board sequester, your senior staff appears to be suggesting a course of action that could actually be more harmful to our national security and domestic priorities,” the four GOP leaders wrote.

The sequestration cuts may start next Jan. 2 and cut $1.2 trillion in projected spending, roughly $500 billion of which would come from planned Pentagon funding over the next nine years. The cuts come as a result of the Budget Control Act of 2011. While the administration and many lawmakers object to the cuts, they have not agreed yet on an alternate budget-cutting plan. The first year of cuts would total $110 billion, split between defense and non-defense spending.

Boehner, Cantor, McConnell, and Kyl noted to Obama that a six-month delay in starting the sequestration cuts would not reduce the $110 billion figure.

“In fact, such a delay would actually exacerbate the cut’s impact since agencies would be forced to absorb the same cut in the three remaining months of the fiscal year rather than over nine months,” they said, because fiscal years end on Sept. 30. “Other than pushing sequestration farther away from this November’s election it is difficult to understand what benefit would be derived from a six-month delay.”

They cited proposals from Republican lawmakers to replace sequestration cuts, through steps including federal-workforce reductions.

Obama previously threatened to veto any legislation that tinkers with the sequestration cuts without replacing them with a new full-blown budget-cutting plan.

The Republican leaders asked Obama to work with them to “find common ground.”

“Rather than proposing to simply put more space between this problem and the election or offering tax increase proposals that face bipartisan Congressional opposition, we hope you instead work with us to find a bipartisan solution before the end of the fiscal year,” they wrote in their July 13 letter.

The White House did not have an immediate response last Friday.

While Republicans have typically rejected Democrats’ calls to include new revenues in any budget plan to replace the sequestration cuts, some GOP lawmakers have said recently they would consider some revenue raisers other than tax-rate increases.

Senate Armed Services Committee Chairman Carl Levin (D-Mich.) and Ranking Member John McCain (R-Ariz.) have been meeting with lawmakers including Sen. Lindsey Graham (R-S.C.) about crafting an alternate-sequestration plan.

“We’re working to find the necessary $109 billion to replace sequestration for defense and non-defense spending,” Graham said in a statement last Friday. He recommended taking proposals from the so-called Simpson-Bowles commission, which recommended increasing fees and eliminating some tax earmarks.

“However, the vast majority of the reductions would come from reducing the size of government,” Graham argued. “Tax rate increases are not necessary to solve this problem and will do damage to our economy.”