Republicans in the U.S. Congress turned in earnest on Monday to their biggest challenge of Donald Trump's presidency: trying to bridge internal divisions over proposed cuts to Medicaid and popular green energy initiatives to pay for a landmark tax-cut bill they hope to enact by July 4.

WASHINGTON—Republicans pushed President Trump’s “big, beautiful” tax and spending package closer to the finish line with votes earlier this month approving a budget framework. But as lawmakers return to work this week,