Debt limit looms as Senate Minority Leader Mitch McConnell talks with Treasury Secretary Janet Yellen

The debt limit was part of a call between Treasury Secretary Janet Yellen and Senate Minority Leader Mitch McConnell on Wednesday, a person familiar with the conversation told CBS News. As the U.S. barrels closer toward running out the cash to pay its bills, Yellen has warned inaction would lead to catastrophic economic consequences. 

The United States could hit the so-called X-date — when measures keeping the government running are exhausted — as soon as next month, leading to the government to default on its debts. But McConnell has said Republicans would not vote to raise the debt ceiling. 

"With a Democratic President, a Democratic House, and a Democratic Senate, Democrats have every tool they need to raise the debt limit. It is their sole responsibility," McConnell tweeted Wednesday. "Republicans will not facilitate another reckless, partisan taxing and spending spree."