Senate Majority Leader Mitch McConnell said Sunday that the Republican-controlled Congress won’t allow the government to default as the Treasury Department quickly approaches its so-called “debt ceiling.”

“I made it clear after November that we won’t shut down the government or default on debt,” the Kentucky Republican told CBS’ “Face the Nation.”

McConnell’s promise came two days after Treasury Secretary Jack Lew told Capitol Hill that the government loses its authority after March 15 to borrow money to cover approved congressional spending and that his agency would have to resort to “extraordinary measures” as a short-term solution.

To be sure, McConnell acknowledged after winning a tough midterm election bid that voters were tired of an ineffective Congress that too often teetered on shutting down the government over bipartisan issues.

“I hear your concerns,” McConnell said in his victory speech.

Still, Congress came perilously close in recent weeks to at least partially closing the Department of Homeland Security when Republicans tried to tie funding for the agency to efforts to roll back President Obama’s executive actions on immigration.

Lew told Congress on Friday that he will start using the package of emergency measures he has used in the past to keep the federal government from going over the debt limit next week.

The debt limit has been suspended for the past year, meaning that Treasury could borrow as much as it needed to keep the government running. But the limit will go back into effect on March 15 at whatever level of debt exists at that point.

The nation's debt currently stands at $18.1 trillion.

Treasury can employ certain accounting measures to buy time to keep the government operating without facing a costly default on the nation's debt.

In his letter to congressional leaders on Friday, Lew said he would use the first of those measures on March 13, two days before the debt limit will be re-imposed.

Lew said he would stop issuing on March 13 special-purpose Treasury debt that can be purchased by state and local governments to assist them in financing such activities as construction projects.

The Congressional Budget Office, in a report last week, estimated that the various measures Lew can employ could put off the date the debt ceiling will have to be raised until October or November.

McConnell also told CBS on Sunday that Congress will handle the issue “over a period of months” and that he has a responsibility to work with President Obama, despite their political differences.

He also said he is “very optimistic” about potential compromises with Obama on some issues.

“The American public wants us to look at what we can agree on,” McConnell said.

It was a standoff over the debt limit in August 2011 that prompted the first-ever downgrade of the nation's credit rating by Standard & Poor's, and in October 2013 there was a 16-day partial government shutdown.

"Only Congress is empowered to increase the nation's borrowing authority and I hope that Congress will address this matter without controversy or brinksmanship," Lew said in his letter. "I respectfully ask Congress to raise the debt limit as soon as possible."

While GOP lawmakers have given no indication when they will take up legislation to increase the debt ceiling, House Democratic Leader Nancy Pelosi on Friday urged them to move quickly, warning that an unprecedented default by the government on its debt obligations would severely harm the economy by causing consumer and business interest rates to soar.

"There is no reason that the Republican Congress should not act immediately to take the prospect of a catastrophic default off of the table," she said in a statement. "Failure to act would have savage impacts on American families."

The Associated Press contributed to this report.