The House is expected to weigh this month a new bill from the House Budget Committee chairman to start undoing planned “sequestration” cuts to the Pentagon’s budget.

The bill, which Chairman Paul Ryan (R-Wis.) filed in the House last Friday, is intended to prevent the first year of cuts to defense and non-defense spending, which total $1.2 trillion over nine years, mandated by a so-called “sequestration” process. The sequestration reductions, which are slated to start next January, were triggered by the failure of a congressional committee to craft a deficit-cutting plan last year.

In addition to the newly filed bill, the House Budget Committee also has crafted a companion piece of legislation, the Sequester Replacement Reconciliation Act of 2012, that details cuts to mandatory programs to make up for the sequestration reductions. Those reconciliation offsets to mandatory spending were recommended by six House committees in reports released Monday.

Ryan’s emerging and multi-part plan to shield the Pentagon and other discretionary parts of the budget from sequestration is not expected to pass the Senate controlled by Democrats. But the effort has strong support in the Republican-led House–from members including House Armed Services Committee (HASC) Chairman Howard “Buck” McKeon (R-Calif.)–and members are expected to vote on it before Memorial Day.

“House leadership is trying to address sequestration now,” said Mackenzie Eaglen, a resident fellow at the American Enterprise Institute’s Marilyn Ware Center for Security Studies. “There is a general sense of urgency on the side of people like Chairman McKeon that have made their case to House leadership that you cannot wait until the lame duck (session of Congress this year after the November election) to deal with that.”

Eaglen, speaking during a Defense Daily webinar on the defense budget last week, joined many observers in predicting Congress won’t address sequestration until that lame-duck session. Yet, she added, lawmakers will have many big items to deal with then, including addressing multiple tax cuts that are slated to expire, and questioned if sequestration will be changed before the cuts are slated to start next Jan. 2.

“The lame duck agenda is packed,” she said. “Sequestration is considered a small-bore item relative to the other things on the agenda that are just as controversial if not much more so.”

Eaglen was pessimistic about congressional Democrats and Republicans reaching a “grand bargain” on reducing the deficit that could render the sequestration cuts moot.

“There’s no reason to think there’s going to be a grand bargain,” she said. “We expect continued divided government. There is no clear mandate for either political party, and so the question now becomes how to address sequestration.”

The supporters of Ryan’s anti-sequestration push include McKeon, who has repeatedly warned of damage he said will be made to the military if the sequestration cuts proceed. Those reductions, which the Pentagon did not factor into its budget for next year, could total $500 billion over nearly a decade and come on top of $487 billion in 10-year spending reductions the military already is planning for.

McKeon introduced earlier this year his own anti-sequestration legislation, which seeks to reduce the federal workforce to prevent the first year of the $500 billion, nine-year cuts. Yet he told reporters last week he is throwing his support behind Ryan’s multi-part plan.

“The play right now (with) the leadership is the Ryan budget, the reconciliation, and that’s where we’re putting our efforts,” McKeon said last Wednesday after a speech on his priorities for the fiscal year 2013 defense authorization bill. “I want to do all I can to help, because that’s the most viable (plan).”

McKeon noted the House-passed budget resolution, crafted by the House Budget Committee, would not reduce planned defense spending next year as much as President Barack Obama’s budget would. The HASC is using that resolution as a guide for crafting the FY ’13 authorization measure, which aides said includes $4 billion in spending above the Pentagon’s official budget request. The full HASC will mark up that authorization bill next Wednesday.