But the New York Democrat warned President Donald Trump not to insist on "poison pill amendments" that could disrupt negotiations that are underway.
Schumer's relatively upbeat tone matches that of other leaders and top aides who in recent days have said they are hopeful a deal could be approved and a politically perilous shutdown avoided.
"If the President doesn't interfere and insist on poison pill amendments being shoved down the throat of the Congress, we can come up with an agreement," Schumer said in a conference call with reporters. "Our Republican colleagues know that they control all -- the House, the Senate and White House -- and that a shutdown would fall on their shoulders and they don't want it. We want to make sure it's a good budget that meets our principles. But so far, so good."
Schumer said Democrats would insist that a final package include continued government subsidies for lower income users of the Affordable Care Act, rejecting a suggestion by Trump last week
that those payments be withheld in an effort to force Democrats to negotiate the repeal and replacement of Obamacare.
"Negotiations seem to be going quite well," Schumer said about the subsidies issue. "I'm very hopeful we can come to an agreement that everyone can be proud of. I'm not going to get into details but we're working hard to get that provision in."
Schumer also said Democrats would reject any funding for the Trump's proposed border wall with Mexico
in a final package and said other funding for immigration reform issues should be put off to next year's budget.
"We think that the immigration issue should be discussed in the 2018 budget," he said. "Nothing should be shoved down people's throats. That would apply to the many immigration issues that are before us. Not just the wall."
A GOP aide said last week that increased funding for Customs and Border Patrol and Immigration and Customs Enforcement might be part of the final bill. But Schumer's comments indicate Democrats don't agree.
In his call, Schumer reiterated what he first said a week ago -- that Trump's refusal to release his tax returns will make it harder for Congress to pass a tax reform deal, which is a top GOP priority.
"What I've said is it's going to be much harder to get tax reform done if the President doesn't disclose his taxes," Schumer said. "For the very simple reason that when there is a provision in the bill, people are going to say, 'Oh, this is for President Trump and his business, not for the benefit of the American people.' Particularly when you have the sort of large real estate business that he has. There are all kinds of tax laws that affect it. If the President is interested in tax reform, he should release his tax returns because it's going to make it much harder to pass it without it."
Schumer's press call was designed to criticize Trump's trip to Wisconsin promoting
his "Buy American, Hire American" themes.
Schumer said to this point in his presidency, Trump has failed to live up to his campaign promises on those and other issues important to wary American workers. He was especially critical of Trump's decision not to declare China a currency manipulator, something candidate Trump vowed to do.
"The President continues to say one thing but do another," Schumer said. "And the American worker continues to get the short end of the stick from this administration."