Oct. 09, 2013 -- No matter how many times President Obama calls for an up-or-down vote, Speaker John Boehner won't budge on the math, insisting since his Sunday morning appearance on ABC's "This Week" that "there are not the votes in the House to pass a clean CR."

Three days later, however, it looks like he still might be wrong, though just barely.

By ABC News' count, at least 219 members (up from 218 Tuesday) say they would support a "clean" measure to extend all government funding without other conditions attached, such as defunding or delaying the president's health care law; 217 of the 432 members is the threshold needed to pass the measure. (Three seats are vacant.)

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How did we get to that number?

On Saturday, 195 Democrats signed a letter to Boehner that said, "Enough is enough. … We demand a vote on a clean continuing resolution immediately so that government functioning can resume and Americans can move on with their lives."

Aides to the five other House Democrats -- Reps. Mike McIntyre of North Carolina, Jim Matheson of Utah, Jim Cooper of Tennessee, Ron Kind of Wisconsin and John Barrow of Georgia -- told ABC News Monday that they would vote for a clean "continuing resolution," or CR.

That makes all 200 Democratic votes for a clean CR.

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Cooper and Kind wrote their own letter to Boehner Monday calling the government shutdown a "real tragedy for America."

"We support a clean CR," Kind and Cooper wrote. "There is more than enough bipartisan support in the House to pass a clean CR and reopen the government. … Democrats and Republicans are supposed to compromise and work together for the good of the country."

According to ABC News' count, there are at least 19 Republicans who have publicly said they would support a "clean" CR if it were brought to the floor.

Aides to 14 of the 232 GOP members have told ABC News their members of Congress would support a "clean" CR. They are: Reps. Mike Coffman of Colorado; Michael Grimm of New York; Jim Gerlach of Pennsylvania; Peter King of New York; Tim Griffin of Arkansas; Frank Wolf of Virginia; Rob Wittman of Virginia; Scott Rigell of Virginia; Bill Young of Florida; Jon Runyan of New Jersey; Frank LoBiondo of New Jersey; Charlie Dent of Pennsylvania; Dennis Ross of Florida, and David Reichert of Washington.

Five other GOP members -- Reps. Devin Nunes, R-Calif., Lou Barletta, R-Pa., Mike Simpson, R-Idaho, Leonard Lance, R-N.J., and Randy Forbes, R-Va. -- had previously been on record in support of a clean CR, but said Monday and Tuesday either their previous positions were misconstrued or they had changed their minds.

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Why does this number keep changing?

Two of the most recent changes essentially swapped one Republican for another. Barletta's press secretary Tim Murtaugh told ABC News Monday the congressman would support a "clean" CR "should it come up," but Murtaugh Tuesday said Barletta had changed his mind.

"While he once expressed openness to a no-strings-attached CR, a growing number of Democrats have emerged who will support a repeal of Obamacare's medical device tax," Murtaugh said in an email to ABC News. "That would open the government, and also get rid of a job-killing, cost-raising funding source of Obamacare.

"Sometimes being in Congress means pursuing the art of the possible. This would be a CR that can pass the House and Senate."

Rep. Coffman (who's listed in the group of 13 above) Tuesday announced his support for a "clean" CR in an op-ed in the Denver Post and in a statement.

"The debate over attaching Obamacare to a spending bill must end and I will argue before my colleagues in the House that we need to pass a 'clean' spending bill to immediately reopen the government," Coffman, who had not previously weighed in, wrote.

Another recent addition is Rep. Reichert (also listed above in the 13), who said in a statement Monday, "As your Representative, please know that I will continue to vote for any legislation that keeps the federal government open."

Although Reichert did not say it explicitly, an aide told ABC News that "he will continue to support legislation that opens the government."

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Who are the other Republicans who say they support a "clean" CR?

Rep. Patrick Meehan, R-Pa., said in a statement Oct. 1 he "believe(s) it's time for the House to vote for a clean, short-term funding bill to bring the Senate to the table and negotiate a responsible compromise."

Aides to five other Republicans did not return a request for comment, but have publicly said they would support the legislation:

Rep. Walter Jones, R-N.C., said on MSNBC Tuesday, "I wish we would pass a clean CR. People are beginning back home to feel it. It might be imaginary, but they feel it."

Rep. Erik Paulsen, R-Minn. told local NBC station KARE 11 that if he "had an opportunity just to vote to fully fund the government, I would do that."

Rep. Richard Hanna, R-N.Y., told the Observer-Dispatch that he "would take a clean [continuing resolution]."

Rep. Mike Fitzpatrick, R-Pa., told the Philadelphia Inquirer he would back a "clean" spending bill at current funding levels.

"Americans want their government to remain open and want to see public officials resolve our differences to put our country back on the right track," Fitzpatrick said in a statement to the newspaper.

ABC News' Abby Phillip, John Parkinson and Rick Klein contributed to this report.