"We will not fund states that allow anarchy," she told reporters.
The federal government remains closed amid a bitter impasse on Capitol Hill over competing congressional spending bills.
President Donald Trump and Republicans have cast blame for the shutdown on Democrats' health care demands, while Democrats insist Republicans need to negotiate.
The Trump administration has threatened mass layoffs of some federal workers during the shutdown.
The Democrat funding bill that includes health care provisions failed to pass again on Wednesday morning by a vote of 47-53. Once again, every Democrat voted for it and every Republican voted against it.
-ABC News' Allison Pecorin
House Democratic leaders said they are "willing to negotiate" on a way to end the government shutdown "if Republicans are serious about addressing the health care crisis they have created."
"Republicans control the Senate, the House and the White House. They need Democratic votes to fund the government, so it's on them to talk with us," House Democratic Caucus Vice-Chair Pete Aguilar said on Wednesday.
Aguilar also criticized House Speaker Mike Johnson, saying his word "doesn't mean much to House Democrats" and he is "simply focused on doing what his conference wants."
He called the shutdown a "shame" and know that "this is a disruption" for many people.
"Let's avoid this shutdown, let's end this," Aguilar said.
Construction of the White House ballroom will continue through the government shutdown, according to a White House official.
"There will not be a stoppage of ballroom work when the shutdown occurs," a White House official told ABC News.
As the White House Office of Management and Budget laid out in a memo last week, programs and projects with sources of funding not related to the appropriations that have lapsed will continue. The White House has previously said that the construction of the ballroom is funded by private donations.
"Work will continue to be performed as the funds currently supporting are not tied to a FY26 enacted appropriation," the White House official said.
-ABC News' Michelle Stoddart
Washington, D.C., Mayor Muriel Bowser announced on Wednesday that the city will remain open during the government shutdown.
"A federal government shutdown will not shut down the DC Government," Bowser said on Wednesday, noting that the local government will remain open, as is standard during federal shutdowns. She said the city often picks up the slack the longer shutdowns last, which can include collecting trash and issuing marriage licenses.
"DC will remain open, our students will be in class, our parks will be clean, our streets will be safe, and we will continue to function as a world-class city no matter what happens in Congress," Bowser said.
She said "no service changes or lapses in benefits are expected" but that "may change depending on future guidance issued from the federal Office of Management and Budget."
Furloughed workers who are impacted by the shutdown can "file for unemployment insurance benefits through the Department of Employment Services," Bowser said.
She added that residents who "depend on federally-supported benefits for medical care, food, and other critical services can and should continue to see their doctors, take their medicines, and buy groceries."
