(Adds Schumer quotes on meeting)
WASHINGTON, Jan 19 (Reuters) - Democratic Senate leader Chuck Schumer met with President Donald Trump at the White House on Friday to search for ways to avert a U.S. government shutdown, but Schumer said afterward that disagreements remained as the clock ticks toward a midnight deadline to pass a funding bill.
Trump invited Schumer to the White House as a stopgap bill to fund the federal government through Feb. 16 appeared on the verge of collapse in the Senate, where Democratic votes are needed to pass it.
"We had a long and detailed meeting," Schumer told reporters at the U.S. Capitol after the meeting, which lasted more than an hour. "We discussed all of the major outstanding issues. We made some progress, but we still have a good number of disagreements. The discussions will continue."
The Republican-controlled House of Representatives approved the stopgap spending measure late on Thursday, but it has been sidetracked in the Senate by a dispute over immigration. The House had planned to recess later on Friday for a weeklong break but members were warned they could be called back for votes.
White House budget director Mick Mulvaney said on Thursday he was ratcheting up the likelihood of a government shutdown from 30 percent to a 50-50 possibility.
Congress has been struggling for months to agree on long-term government funding levels and the immigration issue. The federal government is operating on a third temporary funding measure since the new fiscal year began in October.
Democrats have demanded the bill include protections from deportation for 700,000 young undocumented immigrants. Those children, known as "Dreamers," were brought into the United States as children, largely from Mexico and Central America, and given temporary legal status under a program started by former President Barack Obama. Many have been educated in the United States and know no other country.
In September, Trump announced he was ending the program and giving Congress until March 5 to come up with a legislative replacement.
Markets were keenly focused Friday on the budget woes. The U.S. dollar moved to a near three-year low around midday while Wall Street largely played down any fears of the looming possible shutdown. The Dow opened higher and was down about nine points in mid-afternoon trading.
Leaders of both parties blamed each other for the showdown.
"Now that were 13 hours away from a government shutdown that Democrats would initiate and Democrats would own, the craziness of this seems to be dawning on my friend the Democratic leader," Senate Republican leader Mitch McConnell said, referring to Schumer.
Dick Durbin, the No. 2 Democrat in the Senate, said Republicans needed to sit down and negotiate and called on House Republicans not to leave town until the crisis was averted.
"I would beg them, dont turn your back on your responsibility right here in Washington to work with us, to try to find a way forward," Durbin said.
Trump, on the eve of the first anniversary of his inauguration, said in a morning tweet that Democrats were holding up a resolution over the immigration issue.
"Democrats are needed if it is to pass in the Senate - but they want illegal immigration and weak borders. Shutdown coming?" he said.
Republicans also control the Senate but with Senator John McCain undergoing cancer treatment at home in Arizona, they will need at least 10 Democrats to reach the 60 votes required to pass a spending bill. In addition to strong Democratic opposition, at least three Republican senators have said they will not back the continuing resolution in its current form.
Republican Senator Mike Rounds, who had earlier said he could not back the bill in current form, on Friday said in a statement that while the measure was "not ideal," he would support it after being assured that other legislation to adequately fund the U.S. military would be raised soon.
Democratic Senator Joe Manchin of West Virginia has indicated he was leaning in favor of the stopgap measure. Manchin is one of 10 Democrats up for re-election this year in states Trump won in the 2016 presidential election.
When the government shuts down, which has only happened three times in a meaningful way since 1995, hundreds of thousands of "non-essential" federal workers may be put on furlough, while "essential" employees, dealing with public safety and national security, would keep working.
Amid the deadlock, more senators were raising the possibility of merely approving enough new federal funds for a few days. The idea is to put pressure on negotiators to then cut deals on immigration, defense spending and non-defense funding by next week.
But McConnell shot down that plan on Friday. "Let's fund the government for a full month so we can actually get something done" and negotiate other issues including immigration, he said.
Since then, however, the president has had a series of spats with Congress. Trump and conservatives in Congress have used the Dreamer fight to try to win tough immigration controls, including the president's promised border wall.
Durbin, who is leading the fight for the Dreamers, told reporters late on Thursday there had been some signs earlier in the day that talks with Republicans were taking a positive turn and a deal could be within reach. (Reporting by Richard Cowan; Additional reporting by Roberta Rampton, Steve Holland and Amanda Becker; Editing by Chizu Nomiyama and Bill Trott)