ABC News' Shushannah Walshe and Alex Lazar report:

Speaker John Boehner told ABC's George Stephanopoulos on "This Week" Sunday that " there are not the votes in the House to pass a clean CR," meaning he did not believe a majority of House members would support continued funding for the government without conditions attached.

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It looks like he might be wrong, but just barely.

By ABC News' count, 217 members 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 is the threshold needed to pass the measure.

John Boehner Remixed and 'Ready for a Conversation'

The president today urged Boehner to bring the bill to the floor, telling him to "prove" there are not enough votes.

"If Republicans and Speaker Boehner are saying there are not enough votes, then they should prove it," Obama said. "Let the bill go to the floor, and let's see what happens. Just vote. Let every member of Congress vote their conscience, and they can determine whether or not they want to shut the government down."

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 today that they would vote for a clean "continuing resolution," or CR. That makes 200 Democratic votes for a clean CR.

Cooper and Kind wrote their own letter to Boehner today 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."

Also, according to ABC News' count, there are 17 Republicans who have publicly said they would support a "clean" CR if it were brought to the floor.

Aides to 12 GOP members have told ABC News the members of Congress would support a "clean" CR. They are: Reps. Lou Barletta of Pennsylvania; Michael Grimm of New York; Jim Gerlach of Pennsylvania; Peter King of New York; Tim Griffin of Arkansas; Frank Wolf of West Virginia; Rob Wittman of Virginia; Scott Rigell of Virginia; Bill Young of Florida; Jon Runyan of New Jersey; Frank LoBiondo of New Jersey; and Dennis Ross of Florida .

Four other GOP members - Reps. Devin Nunes, R-Calif., 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 today either their previous positions were misconstrued or they had changed their minds.

But Rep. Patrick Meehan, R-Pa., said in a statement 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 four other Republicans did not return a request for comment, but have publicly said they would support the legislation:

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. Charlie Dent, R-Pa., told the Huffington Post, "I'm prepared to vote for a clean CR."

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.

This story has been updated to move Rep. Leonard Lance, R-NJ, from supporting a clean CR to being against the possible measure.