Sen. Richard Shelby of Alabama, the Republican chairman of the powerful Senate Appropriations Committee, says discussions about ending the stalemate over government funding are "getting nowhere," warning that the shutdown "could last a long, long time."

"Our negotiations are at an impasse at the moment," Shelby said on "Face the Nation" Sunday. "We've got to move away from the blame game." He noted that Senate Majority Leader Mitch McConnell would not "even take up the bill until he found some compromise that the president would agree to sign."

"Whether it's the president tweeting and blaming somebody or blaming the Democrats or whether it's the Democrats blaming the president, it's brought us to the impasse that we are today," Shelby said.

The partial government shutdown has entered its second week, with President Trump and congressional Democrats still at odds over funding for a U.S.-Mexico border wall. The length of the shutdown is approaching some of the longest shutdowns in American history, although not nearly as long as one the longest, which lasted 21 days from December 1995 to January 1996. Any government shutdown, however, can significantly affect government agencies and federal workers, many of whom are working without a paycheck.

According to the latest Reuters poll, 47 percent of Americans blame the president for the shutdown, while 33 percent blame Democrats.

Shelby said Washington is currently at "a standoff" on the issue. He expects the political equation to change after Jan. 3, when Democrats take control of the House and Nancy Pelosi is expected to become House Speaker. "We're going to have to negotiate," he said. "We ought to see, what do the Democrats really want?"

"We've got to show them what we want is to secure the borders," he said.

Shelby, who has spent years on the Senate Banking Committee, also weighed in on the volatility in financial markets, saying "we're all concerned about the economy" and that the Federal Reserve is "set up to be independent."

"The Federal Reserve is the bedrock of our financial system," he said. "I don't believe in blaming the Federal Reserve for this or that."