"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."
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.