"Shutdowns hurt our hard-working federal employees and federal contractors who do the important work on our national security, border security, working with our military, ICE agents, veterans, medical researchers and more", she said.
Trump has repeatedly said this week that he would force the government to shut down if Democrats do not agree to significant increases in border spending, including money to build a wall along the southern border with Mexico, along with changes to the legal immigration system.
Trump wants to put a stop to illegal immigration and has made several inflammatory statements in the past about Mexicans, branding them criminals and "rapists".
But like Trump, some Republican rank-and-file lawmakers are itching for a political fight with Democrats over immigration and border security, believing such a battle would energize conservative voters to turn out in the November elections, where the GOP's House and Senate majorities are at stake.
Democrats consider Comstock among the most vulnerable Republicans in the House this year because Trump lost her district by 10 percentage points in 2016, and polls show he remains deeply unpopular in the Washington suburbs she represents.
White House Deputy Press Secretary Hogan Gidley told reporters that he discussed the issue with the president.
Taylor is the latest Republican to publicly oppose Trump's threat. In fact, according to the Pew Research Center, Congress has only ever passed all its appropriations bills by the deadline (which was created in 1976) four times - in 1977, 1989, 1995, and 1997.
But the president has been anything but patient, taking to Twitter on Sunday, Monday and Tuesday to say he's ready to have a government shutdown unless he sees action on his immigration priorities. Because Trump's wall was funded during the current fiscal year, it would continue for the length of the extension. Before leaving for the August recess, House appropriators approved $5 billion for 200 miles of border wall, funds scraped from raiding budgets of other homeland security agencies such as the Coast Guard.
"I understand it", he said.
Schumer said he hopes Trump will stay out of the talks and leave it to Congress to do their constitutional job of funding the government.
A shutdown when government funding expires at the end of September, just weeks before the midterm elections, would be the third under unified Republican control of Washington, following stoppages in January and February.
The notion of a government shutdown was criticized by Senate Appropriations Committee Chairman Richard Shelby. "It's mind boggling to me that anybody would say, 'well, we're going to shut down the government if I don't get my way". "The political ramifications of a shutdown as everybody here knows is not good for either party, it's not good for America".