WASHINGTON—President Donald Trump is set Monday to unveil a program to transform how the nation’s infrastructure is funded and developed, but the initiative faces an uncertain road in Congress over finding the money to pay for it.

Mr. Trump will propose spending $200 billion over 10 years, most in the form of new, competitive grants designed to encourage states and cities to raise their own money for improving rails, airports, highways and water systems. The proposal also would expand federal loan programs for such projects.

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