House GOP leaders are lining up behind the conservative Republican Study Committee to support additional spending cuts next week when the 2011 continuing resolution reaches the floor. But even with leadership on board, will it be enough to hit the magic number of 218 votes?

Under a process not seen in years, members will be able to offer amendments to the CR under an “open rule.” Conservatives, lead by Rep. Jim Jordan (R-Ohio), will offer one that achieves a full $100 billion cut in non-security discretionary spending. Last week GOP leaders put forth a plan that cuts $58 billion from the current fiscal year.

The RSC got a boost yesterday when Majority Leader Eric Cantor (R-Va.) announced he would vote for additional cuts beyond the GOP’s initial $58 billion proposal. Last week his spokesman singled out the RSC as a group likely to propose additional cuts that Cantor would support.

“There has been a lot of talk on our side that members want to cut even further, and most of us welcome that talk and will be supporting yet even further cuts,” Cantor told reporters yesterday. He later added: “I’m going to be supportive of a lot of the amendments.”

It’s likely that Speaker John Boehner (R-Ohio) would support additional cuts, but he has not declared his intentions because members are still drafting amendments.

Other GOP leadership offices have followed Cantor’s lead. Majority Whip Kevin McCarthy (R-Calif.), Conference Chairman Jeb Hensarling (R-Tex.) and Chief Deputy Whip Peter Roskam (R-Ill.) all favor more spending cuts.

That’s good news for the RSC. But it still might not be enough to push the RSC’s $100 billion amendment over the top.

Assuming the RSC has the backing of its 175 members, it will need to pick up an additional 43 votes. While some moderate Democrats might be inclined to support the RSC amendment, Republican appropriators could play spoiler.

Yesterday 27 Republicans on the House Appropriations Committee backed the leadership plan. But there were two notable defections: Reps. Jeff Flake (R-Ariz.) and Cynthia Lummis (R-Wyo.) voted against the bill because the cuts weren’t deep enough.

Now that it heads to the floor, it’s unclear how those appropriators will vote — or if they’ll be nudged by leadership.

Then there’s the additional challenge of competing against potentially hundreds of other spending cut amendments, many of which won’t come close to what the RSC plans to propose.

Regardless of how much is ultimately cut, Cantor celebrated the fact that the tone had already shifted in favor of spending cuts.

“We said we were going to change the culture in Washington and I don’t think any of us can really remember a time in which we were really bickering about the levels of spending cuts,” he said yesterday. “We were always faced with an environment where we were growing spending. So in that way I do think we have begun to make some progress on our commitment to change the culture in Washington.”

That much is true.