WASHINGTON—Elon Musk gave new fuel to GOP critics of the Republicans’ multitrillion-dollar tax and spending agenda, saying that the current measure failed to reduce the federal deficit, echoing complaints from hard-line factions in both the House and the Senate.

Republicans are rushing to pass the bill — which would cut taxes and spending, raise the debt limit and increase defense and border security funding — by July 4. The true deadline might be later this summer, when the federal government expects to exhaust its borrowing capacity.