Today, House Republicans are set to hold another series of votes on still more piecemeal measures funding the government — the latest move designed to minimize the political fallout of the continued shutdown. Senate Dems will reject them, and the White House just announced that Obama would veto the measures in any case.

It’s worth reiterating that all of those “moderate” House Republicans who say they want to vote on a “clean CR” funding the government — but can’t, because the House GOP leadership won’t allow such a vote — could probably help reopen the government right now if they really wanted to. They could certainly do a lot more to help bring this about.

According to the Huffington Post’s latest count, at least 22 House Republicans want a vote on a clean CR.

Democrats on the House Rules Committee point out that there is a procedure by which those Republicans could actually help bring about such a vote. It turns on what is known as a “previous question.” The idea is that before the House votes to bring up the piecemeal measures that are getting considered today, there is first a full vote on the “previous question,” which is effectively a vote to proceed with the majority’s agenda (in this case, the piecemeal bills). If those moderate Republicans were to vote No, along with all House Dems, on this procedural vote, adding up to a majority, this would shift control of the floor to the ranking Democrat on the Rules Committee, Rep. Louise Slaughter.

At that point, the Dems could offer its own amendment to the “rule,” which would in this case be an amendment to bring up the Senate “clean CR bill.” It would get a vote, and if those moderate Republicans made good on their public statements in favor of a clean CR, it would pass the House. Today, Rep. Slaughter will again call on those moderate Republicans to join Dems in this procedural move, as she has vainly done for days now.

“Put your voting card where your mouth is,” Slaughter will say today on the floor.

Needless to say, it is highly unlikely to happen, since those moderate Republican would be loath to buck the GOP leadership. And as many others have noted, this has not worked yet.

But it’s worth pointing out that there is a precedent for this maneuver working. According to Rules Committee Dems, Republicans successfully used the tactic against the House Democratic majority back in the early 1980s. President Ronald Reagan was trying to get a budget measure through, and Dem House Speaker Tip O’Neill opposed it. But a bunch of conservative Democrats joined with House Republicans to defeat the “previous question,” shifting control of the floor to Republicans, who then passed the Reagan measure.

According to one Congressional historian, Speaker O’Neill had this to say about the move: “I’ve never seen anything like this before in my life, to be perfectly truthful.”

So it’s not impossible this could happen, particularly if these piecemeal votes continue and more moderate House Republicans come out in favor of a vote on the clean CR. Of course, those moderate Republicans would have to get serious about forcing the vote  they say they want.

Oh, and one other thing. We keep hearing that some Senate Republicans — who, you may recall, voted for the clean CR in the Upper Chamber — are unhappy with the current House GOP strategy. It might be worth asking them if they think the House GOP leadership should allow a House vote on that clean CR, then.