Last week, House Majority Leader Eric Cantor (R-Va.) conceded some additional infrastructure investments may be worthwhile, and offered the Obama administration an idea he said could garner bipartisan support. The Hill called it an “olive branch.”

The idea wouldn’t actually spend additional money on much-needed projects that would create jobs, but it would in theory free up some funds. As Cantor argued, there’s an existing rule that says states must set aside 10% of federal surface transportation funds for “museums, education and preservation.” If the rule were waived or scrapped, states could divert those funds to roads and highways. House Speaker John Boehner (R-Ohio) immediately endorsed the plan in a letter to the White House.

As “olive branches” go, this is extremely thin. Worse, the Republican leadership’s idea, like nearly all ideologically-driven ideas, starts with the conclusion — don’t make any additional public investments — and works backwards to satisfy an arbitrary, philosophical standard.

But at least it’s something resembling progress, right? Wrong. The real problem is Boehner and Cantor flubbed the key details.

There is no requirement that states set aside 10 percent of all federal surface transportation funds for purposes of funding Transportation Enhancement projects, a Department of Transportation official confirms. Rather, the law says that they must set aside ten percent of the Federal Highway Administration (FHWA) funding for those purposes.

It’s not a minor distinction. The FHWA — a sub-agency of the Department of Transportation — was appropriated $927.6 million in fiscal year 2011. The funding for surface transportation during that same period was more than $50 billion.

In other words: the Republican proposal would result in about two percent of surface transportation funding being freed up for states to use on their own infrastructure projects. The Transportation Department official adds, for good measure, that the projects funded by the transportation enhancement program are not, as Boehner suggests, a cornucopia of questionably useful, largely scenic items. “It’s almost exclusively bicycle and pedestrian projects,” the official said.

If the GOP leaders are going to try to come with a meaningful policy, they’ll have to do better than this.

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.