WASHINGTON, Nov 21 (Reuters) - Fresh off securing U.S. House of Representatives passage of President Joe Biden"s social and environmental spending plan, his fellow Democrats are pressing ahead with it in the Senate, where the bill may undergo major changes on issues such as paid family leave to satisfy party centrists. The $1.75 trillion legislation, approved by the House on Friday over united Republican opposition, includes four weeks of family leave paid by the government for reasons such as the birth of a child or caring for a sick relative. It is likely to become a battleground issue in the days ahead. The legislation, which aims to bolster the U.S. social safety net and fight climate change, must win over divided Senate Democratic moderates and liberals, as Republicans remain opposed. Democrats have said they want an agreement by year"s end. Any Senate changes would need House approval again. "There"s going to be some changes," Democratic Senator Jon Tester told NBC"s "Meet the Press" program, urging compromise. "We don"t all see the world the same way." Biden has said he looks forward to signing the bill into law as soon as it passes Congress, which is narrowly controlled by the Democrats. The bill must secure support from the 100-seat Senate"s 48 Democrats and the two independents who caucus with them because no Republican backs it. Centrist Democrats Joe Manchin and Kyrsten Sinema in particular have raised concerns about its cost and scope. Democratic Senator Kirsten Gillibrand mentioned differences with Manchin over paid family leave but said she hopes they could reach a compromise in the next three weeks. "This is the only moment to get paid leave done. ... Now is the time," Gillibrand told CBS"s "Face the Nation" program. The cost of the four weeks of federal paid leave has been estimated at $200 billion over 10 years. Gillibrand said the legislation could include an employee-employer contribution system similar to those used by some U.S. states. The United States is the only wealthy country that does not pay woman on maternity leave. The White House is reaching out to lawmakers to get the legislation passed, Biden"s National Economic Council Director Brian Deese said. "We will work with every member of the Senate on this bill," Deese told the "Fox News Sunday" program, adding that the legislation has "a lot of momentum." "We really do now have a good understanding of where the consensus lies," Deese added, on issues such as government support for childcare costs, family benefits and tax increases on corporations and the wealthy. The House passed the bill with just one Democrat voting against it. It was scaled down from Democrats" original $3.5 trillion vision. Reporting by Susan Heavey; Editing by Will Dunham and Heather Timmons Our Standards: The Thomson Reuters Trust Principles.