US House Republicans introduced a proposal Monday that would fund the government through the end of fiscal year 2013, albeit at a reduced level to account for harsh spending cuts already under way.

The measure, expected to be brought to the floor for a vote this week, does not cancel the $85 billion in arbitrary and automatic cuts known as sequestration that began to take effect last Friday.

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But it takes the sting out of some of the reductions, particularly in the military, by giving departments such as the Pentagon the ability to shift the funds in order to avoid deep cuts to critical operations.

“The legislation will avoid a government shutdown on March 27th, prioritize (Department of Defense) and veterans’ programs, and allow the Pentagon some leeway to do its best with the funding it has,” said House Appropriations Committee chairman Harold Rogers in introducing the bill.

The Pentagon, which is set to endure half of the federal cuts, or roughly $42.7 billion, would see a $10 billion bump to its funding, allowing it to mitigate some of the sequester’s effects, Rogers said.

With the budget cuts mandated by the sequester taken into account, he said total US budget expenditures would be capped at $982 billion for the year, less than the $1.043 trillion agreed to under federal law.

But the bill would not erase many of the cuts to domestic programs that Democrats in particular have railed against — including border enforcement, air traffic control, student and childcare programs and medical research — and which are set to kick in from this month.

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While it would allow a more rational approach to budget carve-outs in the military, “the sequestration is as dumb as ever,” argued Richard Kogan, a budget expert at the Center on Budget and Policy Priorities.

“It is only the defense starting point that is smarter.”

Some Democrats have expressed a desire to replace the budget-funding provision, known as a continuing resolution, with new spending measures that would give social and other domestic programs the said help in coping with sequestration that the military would get under the Rogers plan.

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Under federal law, all US government spending must be authorized by Congress. But the divided lawmakers in Washington have not approved a proper budget since 2009, instead voting on temporary continuing resolutions, usually at six-month intervals, that authorize spending at the previous year’s rate.

In September, Congress voted to fund the government until March 27.