WASHINGTON—Elon Musk defended his cost-cutting plans as a common-sense campaign to rein in out-of-control government spending, amid opposition from Democrats and legal challenges that have stalled some of his efforts.

Billionaire Elon Musk and President Donald Trump presented a united front in the Oval Office on Tuesday — before Trump granted Musk even more power. Trump signed an executive order that requires federal agencies to report to the Musk-led Department of Government Efficiency Service as they cut down the federal workforce.