(Adds new DACA court ruling, paragraphs 5-7)
By Richard Cowan
WASHINGTON, Feb 13 (Reuters) - U.S. Senate Republicans on Tuesday turned up the heat on Democrats to accept demands from President Donald Trump for tougher immigration laws and a wall on the U.S.-Mexico border as part of legislation to aid young "Dreamer" immigrants.
Senate Majority Leader Mitch McConnell, a Republican, backed legislation to encompass Trump's "four pillars" of an immigration overhaul, which include plans to build the wall, end the visa lottery program and impose curbs on visas for the families of legal immigrants.
"This proposal has my support and during this week of fair debate I believe it deserves support of every senator who's ready to move beyond making points and actually making a law," McConnell said in a speech on the Senate floor.
The Trump "pillar" of immigration that is easiest for Democrats to accept is protecting some 1.8 million Dreamers who were brought illegally to the United States as children. Many Democrats are reluctant to help fund Trump's long-promised wall, which is aimed at keeping out illegal immigrants but is seen by many lawmakers as too expensive and inefficient.
On Tuesday, a federal judge in Brooklyn, New York, blocked the Trump administration from rescinding on March 5 former President Barack Obama's Deferred Action for Childhood Arrivals, or DACA, program, which protected the Dreamers from deportation. The decision was similar to a ruling last month by a federal judge in San Francisco.
The U.S. Supreme Court is due to consider whether to take up the administration's appeal of the San Francisco ruling and could announce as soon as Friday afternoon whether it will hear the case that is being closely watched by 700,000 DACA participants.
The U.S. Senate began a major immigration debate, its first in nearly five years, on Monday evening. Republicans held a tough line, at least for now, in the search for a bipartisan deal.
Republican Senator Tom Cotton, interviewed on Fox News, said Trump's immigration plan "is not an opening bid for negotiations. It's a best and final offer."
That ran counter to statements Trump had made in recent days, including early on Tuesday when he said in a tweet: "Negotiations on DACA have begun," suggesting he sees room to budge on some issues.
Congress has been unable to pass a comprehensive immigration bill for more than a decade. In 2013, the Senate voted to grant a pathway to U.S. citizenship for millions of illegal immigrants, but the effort died in the House of Representatives.
Some Republican lawmakers have expressed skepticism the kind of fundamental changes in U.S. immigration law sought by Trump can pass the Senate by week's end, despite McConnell's warning of a tight new deadline when he told reporters: "We'll need to wrap this up this week."
The administration proposes cracking down on overall levels of legal immigration and the type of immigrants who would qualify for visas. Trump wants to aim U.S. immigrant visas at high-skilled workers and allow in fewer relatives of legal immigrants.
Standing beside a large photograph of Chloe Kim, who at 17 became the youngest female snowboarder to win an Olympic gold medal, Democratic Senator Dick Durbin said: "Some say there are too many immigrants." Kim is "the daughter of an immigrant who came here with nothing," he added.
Her father, Kim Jong-jin, is a South Korean immigrant who gave up his job as an engineer to focus on his daughter's sporting career.
Durbin told reporters he thought early Senate votes on immigration proposals from both sides could fail to win the 60 votes needed to clear procedural hurdles.
Senators will be forced to move "toward the center with a moderate approach," Durbin said.
Democrats have talked of possibly coupling a pathway to citizenship for Dreamers with additional border security, including the construction of more border fencing and other high-tech tools to deter illegal immigrants.
A group that includes several centrist senators was working on a proposal that would likely include about $25 billion in additional money for border security, said Democratic Senator Bill Nelson.
Trump would want to focus that money on construction of a U.S.-Mexico border wall. Nelson said: "A wall is many things," and could include electronic devices, natural boundaries and drones.
(Reporting by Richard Cowan; Additional reporting by Katanga Johnson and Susan Cornwell in Washington and Dan Levine in San Francisco; Writing by Alistair Bell; Editing by Jonathan Oatis and Peter Cooney)
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