If you have a small savings and are a decent driver you can drop collision insurance (which would be required if you had a loan) and save an extra hundred or two each month.
At some point you should have an emergency fund with 3-6 mo of living expenses. A brand new Honda Fit starts at $16k. That's about a yearly salary of someone making ($7/hr) minimum wage working full time. So that should be in the realm of possibility for someone making more than minimum wage (or in a state with a higher minimum wage).
How expensive is your insurance?? I have a fully comp insurance with 20 million euro liability that's about ~$500 a year. If I dropped that down to a 3rd party liability only it would save me almost nothing.
[1] https://www.insurance.com/auto-insurance/coverage/comprehens...