Treasury Secretary Jack Lew reiterated Tuesday morning that the Obama administration will not negotiate with congressional Republicans over the debt ceiling, but will seek a fiscal bargain with Republicans in funding the government.

Lew appeared on CNBC’s "Squawk Box" the morning after sending House Speaker John Boehner a letter projecting that the Treasury would run out of headroom under the debt ceiling in mid-October. Lew explained that the letter was not a threat, but that “we’re sharing the information we have” and “it means Congress does need to act” to raise the limit.

Lew reasserted several times during his interview with CNBC’s John Harwood that the White House won’t engage in negotiations with Republicans seeking spending cuts or changes to Obamacare in raising the debt ceiling. But he also indicated that the administration remains willing to talk with the GOP about making other large-scale fiscal adjustments in the upcoming government funding showdown that will take place just shortly before Lew expects the debt ceiling to become binding in mid-October.

President Obama is “looking for the sensible common ground” in trying to make sure the government doesn’t shut down when funding runs out on Oct. 1, the beginning of the new fiscal year, Lew said. Lew made sure to distinguish between negotiations over the debt ceiling and over a new budget or continuing resolution, calling the latter “very different from something as fundamental as saying we’ll put the full faith and credit of the United States at risk.”

In negotiating over funding the government, Lew said, Obama is aiming to replace the sequestration cuts with other fiscal savings and “looking for the sensible common ground,” including entitlement reforms and changes to the corporate tax code. Lew said that Obama has “made clear he’s willing to do tough things on entitlements” but that any such changes would “require balance” in the form of tax hikes.

But even in the continuing resolution talks, Obamacare would remain off the table. In response to Harwood’s question whether the Obama administration would accept any defunding or delaying of Obamacare in a bill funding the government, Lew simply responded “no.”

Lew said he has exchanged calls with Boehner and other Republican leaders regarding the coming fiscal showdowns.