WASHINGTON—Senate Republicans’ tax plan would expand the economy but wouldn’t meet the party’s promise that it will pay for itself through faster economic growth, according to an official congressional analysis released on Thursday.

The bill, which includes $1.4 trillion in net tax cuts over a decade, would make up for just $458 billion of that, or less than one-third of its cost, through economic growth, the analysis said. The bill also would increase federal interest costs by about $51 billion over a decade.

That...