The seller's job is to sell the vehicle. Your job is to understand the vehicle, the numbers and the risk before you commit.
Monthly payment is the result, not the starting point
Your payment is created by the selling price, taxes, fees, add-ons, down payment, trade equity, APR, and loan term. If you negotiate only the payment, any one of those inputs can be adjusted to reach the number you requested. That can make an expensive transaction feel affordable.
Long loan terms can hide cost
Stretching a loan from 60 months to 72 or 84 months can reduce the payment while increasing the time you remain in debt and, depending on the rate, the total interest paid. It may also increase the chance that you owe more than the vehicle is worth for a longer period.
Ask for the complete financing picture
Review the amount financed, APR, term, total of payments, cash down, trade credit, and every financed product. Compare outside financing using the same loan amount and term so you are making a fair comparison.
Use the payment as a final affordability check
After you understand the complete transaction, then decide whether the monthly obligation fits your budget. That order keeps affordability important without allowing the payment to hide the actual purchase.
Bottom line
Do not let urgency replace verification. Compare the market, understand the history, inspect when appropriate, review the complete transaction and decide your maximum before emotion takes over.