WASHINGTON — President Obama will not bargain with lawmakers about attaching conditions to an increase in the debt limit, saying Congress has the responsibility to ensure that the nation’s bills are paid and the government doesn’t default, Treasury Secretary Jacob J. Lew said Tuesday.

“The president’s been very clear we are not going to be negotiating over the debt limit,” Lew told CNBC a day after formally notifying Congress that the federal government would run out of borrowing authority in mid-October.

“Congress has already authorized funding, committed us to make expenditures,” he said. “We’re now in the place where the only question is will we pay the bills that the United States has incurred. The only way to do that is for Congress to act, for it to act quickly.”

Lew said there’s broad agreement that the nation should avoid a repeat of the 2011 showdown over the debt limit, which led to the first-ever cut in the U.S. credit rating from Standard & Poor’s. But he acknowledged that there was no plan yet on how to avoid it as Congress prepares to return early next month from its summer recess.

Pressure on the issue was ratcheted up by the Treasury Department’s new estimate of when the U.S. would face a potential default.

The mid-October deadline puts the White House and Congress on a collision course on the debt limit around the same time they are facing the need to enact a new spending bill to keep the government running past Sept. 30. Related to that, Lew said Tuesday that Obama would not accept any delays or cuts in funding for the healthcare reform law.

The nation technically hit its $16.7-trillion debt limit in May, but the Treasury has been using so-called extraordinary measures since then to juggle the federal government’s finances and continue paying its bills.

Lew said in May that lawmakers had until at least Labor Day to raise the debt limit, and some recent estimates have indicated that the nation would not hit the debt limit until November.

But in a two-page letter Monday, Lew informed congressional leaders and every member of the House and Senate that the Treasury would exhaust all its extraordinary measures by the middle of October.

A spokesman for House Speaker John Boehner (R-Ohio) on Monday said that any increase in the debt limit must be offset by budget cuts or spending reforms at least as large as the increase. Some Republicans have insisted on other conditions, including cutting funding for the healthcare law, also known as Obamacare.

Lew said he had exchanged messages with Boehner on Monday and that he had spoken with other congressional leaders about the new debt limit deadline. The House and Senate are scheduled to return from their summer recess on Sept. 9

“As I talk to leaders on both sides, there’s an understanding of the seriousness of this issue,” Lew said. “I don’t think the leaders are in a place where anyone wants a repeat of 2011. I don’t yet see they have a plan to avoid it.”