"You don't get to extract a ransom for doing your job, for doing what you're supposed to be doing anyway, or just because there's a law there that you don't like," Obama said Monday, delivering a similar message in private phone calls later to Republican House Speaker John Boehner and other lawmakers.
Boehner said he didn't want a government shutdown, but added the health care law "is having a devastating impact. ... Something has to be done."
It wasn't clear how long the standoff would last, but it appeared that Obama and Reid had the upper hand.
"We can't win," said Sen. John McCain, R-Ariz., adding that "sooner or later" the House would have to agree to Democrats' demands for a simple, straightforward funding bill reopening the government.
Another veteran Republican, Rep. Tom Cole of Oklahoma, called the shutdown "a big mistake." Interviewed on MSNBC, Cole called on House and Senate negotiations to end the impasse and insisted Democrats should yield on delaying the requirement that individual Americans have health coverage.
The order directing federal agencies to "execute plans for an orderly shutdown due to the absence of appropriations" was issued by White House Budget Director Sylvia Burwell shortly before midnight Monday.
Around the same time, Obama appeared in a video message assuring members of the military they'll be paid under a law he just signed and telling civilian Defense Department employees that "you and your families deserve better than the dysfunction we're seeing in Congress."
Defense Secretary Chuck Hagel said Tuesday that Pentagon lawyers are trying to determine ways for some of the Defense Department's 400,000 furloughed civilians to continue working.
He bemoaned the standoff, telling reporters traveling with him in South Korea, "It does have an effect on our relationships around the world and it cuts straight to the obvious question: Can you rely on the United States as a reliable partner to fulfill its commitments to its allies?"