Rep. Marsha Blackburn (R-Tenn.) said a brief shutdown of the federal government would just be a "slowdown."
In an interview with The Hill, Blackburn said that if Congress fails to reach a deal before Tuesday, it wouldn't really represent a shutdown.
"It wouldn't be a shutdown, it would be a slowdown," Blackburn said.
She suggested it was possible that the House and Senate would reach an agreement several days after the Sept. 30 deadline, meaning a brief shutdown of the government would occur.
She blamed Obama for the lack of a deal, saying he refuses to sit down with congressional Republicans.
"We don't want a government shutdown. ... We have repeatedly invited the president to come sit at the table with us and negotiate," she said. "We have extended an open hand with him, to work with him and repeatedly, repeatedly he has said no."
The Tennessee lawmaker is slated to appear on CBS's "Face the Nation" Sunday morning, the day before the shutdown deadline.