Advocates of reopening the government without Obamacare strings attached are within striking distance today of securing a House majority for a “clean” continuing resolution. But Republican leadership is giving no indication of relenting and allowing a vote that would bring the partial government shutdown to an end on its second day.

Democratic leadership has said it would be able to muster virtually all 200 members of that caucus to vote for a clean CR lasting several weeks. As of this morning, the roster of Republicans publicly advocating that approach had grown to 14.

Those who have publicly endorsed a clean CR are overwhelmingly from the Northeast, generally have somewhat centrist voting records and mostly represent potentially competitive districts. They are Lou Barletta, Charlie Dent, Michael G. Fitzpatrick and Patrick Meehan of Pennsylvania;  J. Randy Forbes, Scott Rigell, Rob Wittman and Frank R. Wolf of Virginia; Frank A. LoBiondo and Jon Runyan of New Jersey; Michael G. Grimm and Peter T. King of New York; Devin Nunes of California and Erik Paulsen of Minnesota.

At least a handful more GOP members were expected to do likewise on a day in which congressional offices were reporting rising numbers of emails and phone calls from people angry and frustrated about the interruption of federal services and the hardening congressional dysfunction.

“It appears we may be getting to a place where there are going to be enough rational Republicans to join with the Democrats and pass what is a continuing resolution, which will fund government, get us open, give us the opportunity over the next six weeks to see if we can come to an agreement for a final resolution for the balance of the year,” Minority Whip Steny H. Hoyer said on CNN.

Since there are three vacancies at the moment, an absolute majority of the House is 217. But Speaker John A. Boehner has been steadfast in declaring that any legislative move to end the spending impasse would need to have the support of a majority of his majority — and, presumably, many more beyond that, since pushing through a bill that closely divides his caucus would threaten the sort of rebellion from his right the speaker has been working all year to prevent.

King, one of the most outspoken GOP members in favor of a clean CR, says the roster of rank-and-file Republicans coming to that view is escalating fast and may be approaching 100 — although many of them will stay behind the scenes until the last possible moment.

There are also about 40 hard-line tea party conservatives who are outspokenly opposing any retreat from the party’s effort to undermine the health care law as a condition of reopening the government. An equivalent number can be counted on to back that cause for the foreseeable future.

That leaves about 50 Republicans in the middle, in theory, with the fate of the shutdown in their hands.

CORRECTION: An earlier version incorrectly had Jeb Hensarling of Texas  on the list of clean CR advocates.