Going into 2011, we knew there were three procedural choke points , at which the threat of a government shutdown was quite real. The first was in early April, when funding for the current fiscal year nearly forced a shutdown. The second was the debt-ceiling vote, which was resolved a few weeks ago.

And then there’s the third one, which is coming sooner than many may realize.

Once lawmakers return to Capitol Hill after Labor Day, they’ll have just a few weeks to approve new appropriations bills before October 1 to avoid yet another shutdown showdown.

At least for now, it appears House Republicans have less of an appetite for brinkmanship.

House Majority Leader Eric Cantor (R-Va.) urged rank-and-file Republicans in a Wednesday memo to avoid brinksmanship in upcoming battles over Washington spending.

The message from the majority leader is an effort to prevent the kinds of fights over government spending that could lead to government shutdowns this fall if Congress cannot agree on legislation to fund the government.

It suggests Republican leaders worry they could take a political hit if there is a government shutdown from voters already irritated over the contentious summer talks on raising the debt ceiling.

Cantor’s plan, at least of this week, is to persuade his caucus to be satisfied with spending levels agreed to in the debt-ceiling deal. “While all of us would like to have seen a lower discretionary appropriations ceiling for the upcoming fiscal year, the debt limit agreement did set a level of spending that is a real cut from the current year level,” Cantor said in his letter. “I believe it is in our interest to enact into law full-year appropriations bills at this new lower level.”

The oft-confused Majority Leader also stressed the importance of economic “certainty” in the private sector, which seemed bizarre given Cantor’s role in holding the debt ceiling hostage for months, contributing to widespread uncertainty.

Nevertheless, the larger point here is that House Republicans don’t appear eager to force yet another contentious confrontation, which is encouraging, at least until GOP leaders change their minds. Rank-and-file Republican members can still throw a tantrum — maybe they’ll demand a Planned Parenthood rider again? — but with GOP poll numbers deteriorating, it seems likely that Republicans don’t see much of an upside to forcing a shutdown, especially since spending levels will be lower than last year anyway.

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Steve Benen

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.