* Schumer on Trump: "like negotiating with Jell-O"
* Trump: "Democrats wanted to give me a nice present" (Adds White House on no immigration negotiations, Schumer, McConnell)
WASHINGTON, Jan 20 (Reuters) - President Donald Trump and Republican lawmakers took a tough stance on Saturday after the U.S. Congress failed to fund federal agencies, saying they would not negotiate on immigration until Democrats help end the government shutdown.
Funding for federal agencies ran out at midnight with no agreement in Congress, meaning the second year of Donald Trump's presidency began without a fully functioning government. Lawmakers failed to resolve an impasse over Democrats' demands to include certain measures, including protections for young undocumented immigrants, in any short-term spending legislation.
U.S. government workers were told to stay home or, in some cases, work without pay until new funding is approved in the first federal government shutdown since a 16-day funding lapse in October 2013.
The Republican-controlled Senate and House of Representatives were holding rare weekend sessions on Saturday, facing a political crisis that could have an impact on congressional elections in November.
"The president will not negotiate on immigration reform until Democrats stop playing games and reopen the government, White House spokeswoman Sarah Sanders said.
Her message was echoed by Republicans in Congress, leading to speculation that Washington could be in for a prolonged battle that has interrupted government services.
Senate Democratic Leader Chuck Schumer gave a stinging portrayal of Trump as an unreliable negotiating partner, saying the two sides came close to an agreement several times only to have Trump back out at the urging of anti-immigration conservatives.
"Negotiating with President Trump is like negotiating with Jell-O," he said on Saturday. "It's impossible to negotiate with a constantly moving target."
Democrats' demand of securing permanent legal protections for 700,000 young, undocumented immigrants as a condition for new government funding, Walden said, was "hostage-taking in its worse form."
The federal government had been running on three consecutive temporary funding bills since the new fiscal year began in October.
Democrats say they have been pleading with Republicans for months to approve the immigration measure as a stand-alone bill and were rebuffed.
Senate Republican Leader Mitch McConnell said a solution to the crisis was "just inches away" but he blamed Democrats for blocking legislation to pass the stopgap funding measure.
One idea being floated by Republicans was to renew government funding through Feb. 8 to end the shutdown, while working to resolve other issues, ranging from immigration, military and non-military spending levels, disaster relief and some healthcare issues.
The partial government shutdown was triggered at midnight on Friday when the Senate failed to agree to a House-passed bill to fund the government through Feb. 16. It drew strong opposition from Democrats and some Republicans.
Despite tough words from some House Republicans, others were providing conflicting messages.
Marc Short, the White House legislative affairs director, told reporters on Capitol Hill: "We are anxious to get a resolution on DACA.
He was referring to the Deferred Action for Childhood Arrivals program that former President Barack Obama created and Trump ended in September. It was providing protection from deportation for the illegal immigrants brought to the United States as children and now known as "Dreamers."
Moderate Republican Representative Charlie Dent predicted the government shutdown will end only when bipartisan legislation is allowed to advance in Congress, even if it angers conservatives. "That's the price of leadership," he said.
The shutdown began a year to the day after Trump was sworn in as president. He portrayed himself as the ultimate dealmaker but his inability to cut a deal despite having a Republican majority in both houses of Congress marks arguably the most debilitating setback for his administration.
"This is the One Year Anniversary of my Presidency and the Democrats wanted to give me a nice present," he said on Twitter.
"Democrats are far more concerned with illegal immigrants than they are with our great military or safety at our dangerous southern border," he said. "They could have easily made a deal but decided to play shutdown politics instead."
Trump said the shutdown showed the need to win more Republican seats in 2018 congressional elections.
House Democratic Leader Nancy Pelosi laid blame on Republicans in a floor speech on Saturday.
"Despite controlling the House, the Senate and the White House the Republicans were so incompetent, so negligent that they couldn't get it together to keep government open," she said.
There had been modest hope on Friday Schumer went to the White House to talk with Trump but the 90-minute meeting ended with no deal and led to frantic meetings that ran through midnight but proved fruitless.
Democrats and many Republicans want to provide permanent legal status leading to citizenship for so-called Dreamers after Trump ordered the DACA program to expire in March.
The immediate impact of the government shutdown was eased somewhat by its timing, starting on a weekend when most government employees normally do not work anyway.
The Defense Department said its combat operations in Afghanistan and other military activities would continue, while federal law enforcement officers also would remain on duty.
The State Department warned that it could have problems processing passports.
Trump's administration also said it planned to keep national parks open with rangers and security guards on duty. The parks were closed during the last shutdown in 2013, which upset many tourists and resulted in the loss of $500 million in visitor spending in areas around the parks and at the Smithsonian museums.
But without a quick deal, most day-to-day operations in the federal government will be disrupted. Hundreds of thousands of government employees will be put on temporary unpaid leave, including many of the White House's 1,700 workers.
Parks and open-air monuments remained open in the U.S. capital and on the National Mall preparations were under way for a second multi-city women's rights march. Some tourists appeared unaware of the shutdown while others expressed frustration at lawmakers' failure to reach a deal.
"Its ironic that they get paid - meaning Congress - and the rest of the government doesnt, said Dawn Gaither, 57, a Washington teacher. Thats what we need to do, kick these guys in the tail and get them to work.
(Reporting by Richard Cowan, Ginger Gibson, Ian Simpson, David Brunnstrom, Doina Chiacu in Washington and Rich McKay in Atlanta; Editing by John Stonestreet and Bill Trott)