If there were no central banking system that could create money out of thin air, essentially yes. Of course the government could always borrow as well, but less revenue (and no ability to print money) would necessarily mean less capacity to make debt service payments…so overall, it’s fair to say it would mean less spending, and even more fair to say it would put an upper limit on spending (or at least one much stronger than the useless Congressional “ceiling” we have now.)
For more, see:
Fiat money advocates, aka “Greenbackers”