(Reuters) - The U.S. Congress will be in no hurry to raise the federal government's borrowing limit, Senate Majority Leader Mitch McConnell said on Sunday, but will act in time to avoid Washington defaulting on its debt.

"The debt ceiling will be handled over a period of months," McConnell said during an interview on CBS' "Face the Nation" broadcast.

On Friday, Treasury Secretary Jack Lew asked Congress to raise the statutory cap on borrowing "as soon as possible."

The government is expected to exhaust its borrowing authority around March 15, but it can take emergency steps to continue paying its bills. The non-partisan Congressional Budget Office estimates such steps will be exhausted sometime in October or November.

"I made it very clear after the November (2014) election we're certainly not going to shut down the government or default on the national debt," McConnell said.

Even so, Congress is emerging from a contentious fight that at one point brought the Department of Homeland Security within hours of having to shut down some of its operations, as Republicans tied the agency's funding to an attempt to block new immigration policies by President Barack Obama.

Several Republican lawmakers have already predicted the battle over the debt limit could become even more difficult than the DHS funding fight.

Small-government Tea Party activists, who make up a vocal part of Republican ranks, could try to link the debt limit to legislation that Obama and his fellow Democrats in Congress might balk at.

In the CBS interview, McConnell said he hoped a debt limit extension "might carry some other important legislation that we can agree on in connection with it."

He did not provide specifics during the interview, nor did a spokesman after the broadcast.

Since 2011, when Republicans gained control of the House of Representatives, Obama and Congress have tangled over the debt limit, flirting with a possible default.

(Reporting by Richard Cowan; Editing by Tom Heneghan)