Federal government deficit spending works because interest is often higher than return on federal bonds, so it's literally cheaper for the government to go into debt and pay over a long period than to pay cash.
Local government can't do that, but they do have other tools. The one I deal with the most often is Public Improvement Districts where we'll cut a deal to waive municipal property tax or the city's sales tax for like 20 years on a big development in return for the developers building the public infrastructure required to support that development, then transferring it to the City. For really big projects, we may even redirect the tax to the developer, which we actually kinda prefer when that 20-year clock times out and you don't have business owners and residents suddenly getting new taxes they aren't used to and freaking ALL the way out.
It's a deal for the developer because they need that infrastructure anyway, and the only "extra" cost to them is oversizing stuff like wastewater lines beyond what they need, and it's a deal for the city because those road, water, sidewalk, and wastewater extensions they install with the project end up serving more than just that development.