The Obama administration dug in Sunday on its vow to reject proposed spending cuts by congressional Republicans in upcoming budget talks but declined to say whether the president would veto their proposals or allow a government shutdown.

Treasury Secretary Jack Lew told “Fox News Sunday” that President Obama will neither sign government funding bills that slash domestic spending nor negotiate with Republicans over spending cuts to raise the federal debt limit.

However, he would not say whether the president would veto proposals and put the responsibility on Capitol Hill.

“Congress has to do its work," Lew said.

He also repeated what the administration has said in the weeks ahead of talks on short-term funding for federal agencies before a Sept. 30 deadline -- that Capitol Hill lawmakers must replace so-called sequester cuts with less drastic ones.

“Congress should find a way out of sequester,” Lew said.

The across-the-board cuts to Defense Department and domestic spending began in March, after Washington failed to agree on a more even approach.

He also said the president was not going to accept a budget in which domestic spending is further cut to soften the blow to Defense spending.

“That's unacceptable," Lew, who appeared on three Sunday shows to re-enforce the president’s positions, told NBC's "Meet the Press." "He won't sign that."

He told ABC's "This Week" that the president has been "crystal clear" that raising the country's debt limit this fall in non-negotiable.

Congress must pass a so-called continuing resolution before October to fund federal agencies beyond the end of fiscal 2013 and until Washington can agree on a fiscal 2014 budget.

Some conservatives are making a last stand against Obama's new health care law, which includes plans not to fund ObamaCare in the continuing resolution.

Rep. Peter King, R.-N.Y., said Republicans should be searching for ways to de-fund or repeal the Obama health care act. But he called threatening to shut down the government "terror politics" and said the strategy wouldn't work. Others have worried that the gamesmanship could cause Republicans to lose control of the House.

Some observers say it's an idea doomed to fail anyway, since Obama brings both a veto pen and the White House podium to the battle.

"We should not be closing down the government under any circumstances," King said Sunday on CNN's "State of the Union."

Sen. Mike Lee, R-Utah, has taken just that tack, rounding up fellow conservatives to pledge to oppose any budget extension that funds implementation of the health care law.

He told Fox News on Sunday it was unfair to implement a law that many Americans don't want and that still has wrinkles that need to be ironed out.

"I understand that there's some in the Washington establishment, some from both political parties, that weren't happy with me over this. And in this instance, I'm going to take that as a compliment, an indication that I'm doing something right."

Separately, Lew said no federal bailout is in the works for the city of Detroit, which recently filed for bankruptcy protection. Pressed as to why the government chose to bail out big banks, the auto industry and others, but isn't assisting the city, Lew said on CNN's "State of the Union" that the government has been giving Detroit technical advice and has made resources available to help take down blighted properties through federal programs.

But Lew said that the situation during the financial crisis that warranted the other bailouts was "unique," and that the current problems that Detroit has with its creditors, "it's going to have to work out with its creditors."

The Associated Press contributed to this report.