Short answer
It depends on scope, size and phasing, but a full finance and HR replacement for a city or county is usually measured in years rather than months once you include payroll and a stabilization period. The agencies that hit their dates plan around their fiscal calendar, staff the project properly and make decisions quickly.
I am always a little suspicious of a timeline in a proposal, because it usually assumes your team will make every decision on time, your data will convert cleanly and nobody will need to change direction, and none of those things are fully in the vendor's control. Financials alone can move faster than a combined finance, HR and payroll project, and newer cloud products, including some AI-native ERPs in the private sector, are pushing timelines shorter, which I think is going to put healthy pressure on public sector vendors over the next few years.
What really drives the schedule is on your side of the table, so I look at how quickly the agency can make configuration decisions, whether the subject matter experts are backfilled, and whether leadership is willing to settle disagreements between departments rather than letting them drag. Payroll in particular needs time for parallel runs, and I would never compress that to save a few weeks, since a payroll problem is the fastest way to lose the confidence of your employees.
The key to staying on time is to pick go-live dates that respect fiscal year end and budget season, build in a real stabilization period after each go-live, and track decisions as closely as you track tasks. If you do that, the date you announce to council is one you can actually keep.