Even as a winter storm hits the Washington, D.C. area, the U.S. House is to vote by Wednesday afternoon on a Republican plan that is designed to sand down some of the rough edges of $85 billion in across the board budget cuts, and fund the government through the rest of the fiscal year.

The primary change made in the automatic budget cuts is to give the Pentagon more leeway to shift around money in the budget, putting more into the most important accounts for military activities; other agencies also will receive some special language to provide budget flexibility, like the FBI, Border Patrol and NASA.

"This budget does put over $10 billion back into Operations and Maintenance," said Rep. Tom Cole (R-OK), praising the move to give the military the ability to shift money between different military budget programs.

Down Pennsylvania Avenue at the White House, while there was no veto threat, there wasn't exactly a warm embrace for this GOP bill, sending the message that the Obama Administration was "deeply concerned."

Here was the statement from the Office of Management and Budget:

The Administration is deeply concerned about the impact of H.R. 933, making appropriations for the Department of Defense, the Department of Veterans Affairs, and other departments and agencies for the fiscal year ending September 30, 2013, and for other purposes, and is committed to working with the Congress to address these concerns in a way that strengthens the middle class and helps to grow the economy.

While the Administration is pleased to see that H.R. 933 is consistent with the mutually agreed upon budget framework in the Budget Control Act of 2011 (BCA), the bill raises concerns about the Government's ability to protect consumers, avoid deep cuts in critical services that families depend on, and implement critical domestic priorities such as access to quality and affordable health care. Furthermore, while the legislation includes the Department of Defense and the Military Construction and Veterans Affairs and Related Agencies fiscal year 2013 bills, the remainder of Federal agencies are left to operate at last year's level, which will impede their ability to provide services to Americans and efficiently allocate funding to key programs including those in infrastructure, clean energy, education, and research and development.

The Administration looks forward to working with the Congress to refine the legislation to address these concerns. As the Congress considers this bill, the Administration will continue to press the Congress to eliminate the automatic and arbitrary cuts to current funding levels imposed by the Joint Committee sequestration, which will harm middle class and working Americans while costing the Nation's economy hundreds of thousands of jobs. The President continues to work to replace sequestration with a larger, balanced deficit reduction agreement that strengthens the middle class by accelerating job creation and growth while coupling serious entitlement reform that strengthens these critical programs with tax reform that raises revenue by closing tax loopholes for the wealthiest Americans.

The quick action by the House will send this funding bill to the Senate exactly three weeks before a temporary budget plan expires, which will likely push the Senate to amend this plan as early as next week.

"Spending is the problem here in Washington and our goal is to cut spending," said House Speaker John Boehner.

After a lot of grumbling following the fiscal cliff deal, Boehner now seems to have his Republican troops working in unison on this budget plan, as the GOP leadership has vowed to hold the line against any tax increases.

And at this point, tax increases seem unlikely, since the House won't be sending a revenue measure to the Senate; that means even if Democrats attached any tax provisions, they would be ruled out of order in the House.

The House was originally scheduled to vote on this funding measure on Thursday, but that was moved up because of the winter storm.

Maybe lawmakers can blow off some steam after the vote by having a snowball fight out on the Capitol Plaza.