WASHINGTON—House Republicans pushed President Trump’s “big, beautiful” tax-and-spending bill past a key hurdle late Sunday night, but the last-minute grappling has them colliding with a stark reality: The plan won’t reduce federal budget deficits and would make America’s fiscal hole deeper.

A key House committee advanced President Donald Trump’s giant tax and spending package after Republican hardliners won agreement from party leaders to speed up cuts to Medicaid health coverage.The House Budget Committee approved the legislation late Sunday night after a weekend of negotiations with four ultraconservatives on the panel who on Friday joined with Democrats to reject the legislation.