But there is little sign of progress and the Senate, which must pass a deal, has now adjourned until Thursday.
The shutdown began at midnight on Friday after Democrats resisted President Donald Trump’s demands for $5bn (£4bn) for his Mexico border wall.
Neither Mr Trump nor the Democrats show any sign of backing down.
Mr Trump warned there could be “a long stay” in the talks and Democrats told him: “You must abandon the wall.”
Nine of 15 federal departments, including State, Homeland Security, Transportation, Agriculture and Justice began partially shutting down after funding for them lapsed at midnight (05:00GMT Saturday).
Hundreds of thousands of federal employees will have to work unpaid or are furloughed, a kind of temporary leave. This is the third time US federal funding has lapsed so far this year, although the other two were brief.
What’s been happening on Saturday?
The Senate held a rare Saturday session but it was not long before it adjourned.
Republican majority leader Mitch McConnell said the “pause button” had been pushed and that there would be no new Senate vote until he had a signature from the president – and agreement from the Democrats – on a budget deal.
Senate Democratic leader Chuck Schumer said a budget bill that had passed the Republican-controlled House on Thursday approving $5.7bn (£4.5bn) of funding for the wall would “never pass the Senate, not today, not next week, not next year”.
He added: “So Mr President, if you want to open the government, you must abandon the wall, plain and simple.
“The Senate is not interested in swindling American taxpayers for an unnecessary, ineffective and wasteful policy.”
In a tweet on Saturday, Mr Trump said “we are negotiating with the Democrats on desperately needed border security” but the talks “could be a long stay”.
He again defended the wall, saying “the crisis of illegal activity at our southern border is real and will not stop until we build a great steel barrier or wall. Let the work begin!”
One White House official said the administration hoped the shutdown would last only a few days but it could be longer, while Vice-President Mike Pence said negotiators were still talking.
Some Republican lawmakers still hope there can be a deal, perhaps involving less money for the wall.