begins@ (Adds Cornyn comment, Durbin quote, Wall Street reaction)
WASHINGTON, Jan 21 (Reuters) - U.S. Senate Republican and Democratic leaders met on Sunday amid a flurry of congressional negotiations aimed at breaking an impasse that has kept the U.S. government shut down for two days, but it was unclear if a deal could be struck to reopen federal agencies by the start of the work week.
The high-level meeting followed discussions among a bipartisan group of moderate senators who said they made progress toward a compromise, although there was no word of an immediate breakthrough. The ultimate decision was up to Republican Senate Majority Leader Mitch McConnell and Democratic Senate leader Chuck Schumer, they said.
An emerging deal, kick-started by the meeting of about two dozen Republican and Democratic centrists, appeared to involve reopening the government by Monday morning in return for a promise by majority Republicans to deal with Democrats' immigration concerns in coming weeks.
Im hoping they are going to agree to something soon," Republican Senator Jeff Flake said of the McConnell-Schumer talks.
Roy Blunt, a junior member of the Republican Senate leadership, said there was a "chance" of a resolution on Sunday night. But John Cornyn, the No. 2 Republican in the Senate, told reporters when asked if he thought the government would remain shuttered on Monday: "Right now, yeah. I do."
Funding for federal agencies ran out at midnight on Friday, and was not renewed amid a dispute between U.S. President Donald Trump and Democrats over the politically acrimonious issue of immigration.
Refusing to support another short-term government funding extension last week, Democrats demanded that the Republican president live up to an earlier agreement to protect "Dreamers," immigrants brought to the United States illegally as children, from deportation.
"We need to have a substantive answer, and the only person who can lead us to that is President Trump. This is his shutdown," Dick Durbin, the second-ranking Democrat in the Senate, said on the CBS "Face the Nation" program.
'PATH' TO A VOTE?
Later on Sunday, Durbin said Senate leaders were discussing a "path" to a vote to provide legal protection to the Dreamers, although he did not know how far the discussions had advanced.
Trump and other Republicans said earlier on Sunday they would not negotiate immigration or other issues as long as all but essential government services remain shuttered.
"We will not negotiate on the status of unlawful immigrants while Senator Schumer and the Democrats hold the government for millions of Americans and our troops hostage," White House press secretary Sarah Sanders said.
The shutdown is the first since a 16-day closure in October 2013. Its effects will likely be more visible on Monday, when financial markets and federal offices open.
Wall Street gave a muted reaction to the shutdown, with U.S. S&P stock index futures slipping slightly at the open of trading on Sunday night - last down 0.1 percent. Treasury futures prices eased and the dollar index against a basket of currencies was slightly weaker.
The Senate will vote at 1 a.m. (0600 GMT) on Monday on whether to advance a measure to fund the government through Feb. 8, McConnell said on Saturday. But several senators said on Sunday the vote could be accelerated.
"Were going to open the government and solve immigration at the same time," said Republican Senator Lindsey Graham.
Trump, who spoke by phone to Republican lawmakers and agency heads on Sunday but has not had any public appearances since Friday, canceled a weekend trip to his Mar-a-Lago estate in Florida that included a major fundraiser on the anniversary of his first year as president.
The White House said his planned trip to the World Economic Forum in Davos, Switzerland, this week was in flux because of the standoff.
With elections set for November for a third of U.S. Senate seats and the entire House of Representatives, both sides are maneuvering to blame the other for the shutdown.
Trump said earlier on Sunday that if the stalemate continued, Republicans should change Senate rules so a measure could be passed to fund the government.
Current Senate rules require a super-majority of three-fifths of the chamber, usually 60 out of 100, for legislation to clear procedural hurdles and pass.
"If stalemate continues, Republicans should go to 51 percent (Nuclear Option) and vote on real, long term budget," Trump said on Twitter.
But McConnell rejected the idea.
Republicans hold a slim 51-49 majority in the Senate.
'HOSTAGES RIPE FOR THE TAKING'
In a Senate floor speech on Sunday, McConnell accused Schumer of imperiling children's healthcare, military training, veterans' care and other programs.
"To most Americans, those sound like fundamental responsibilities" of government, McConnell said. "To the Democratic leader, apparently they sound like hostages ripe for the taking."
White House budget director Mick Mulvaney said Trump had instructed him to ease the effects of the shutdown as much as possible.
"The president has told me: 'Make sure as many people go to work Monday as possibly can. Use every tool legally available to you,'" Mulvaney said on "Face the Nation."
Amid the sensitive talks to reopen the government, Trump's campaign on Saturday released a 30-second advertisement on immigration.
The ad, posted on YouTube and condemned by Democrats, focused on the ongoing death penalty trial in Sacramento, California, of Luis Bracamontes, an illegal immigrant from Mexico accused of killing two local deputies in 2014.
Schumer and his colleagues accused Trump of being an unreliable negotiating partner, saying the two sides came close to a deal on immigration several times, only to have Trump back out under pressure from anti-immigration conservatives. (Additional reporting by Richard Cowan, Howard Schneider, Patrick Rucker and Makini Brice in Washington and Megan Davies in New York; Writing by Warren Strobel and Matt Spetalnick; Editing by Jeffrey Benkoe and Peter Cooney)