WASHINGTON—Republicans squeaked their budget blueprint through the House late Tuesday after party leaders swayed a handful of wavering members to back the framework for President Trump’s tax, border and spending-cut agenda.

With a push from President Donald Trump, House Republicans sent a GOP budget blueprint to passage Tuesday, a step toward delivering his “big, beautiful bill” with $4.5 trillion in tax breaks and $2 trillion in spending cuts despite a wall of opposition from Democrats and discomfort among Republicans.

House Republicans adopted the budget resolution that will lay the foundation for enacting President Trump’s legislative agenda Tuesday night, just minutes after they initially pulled the