Could I please ask your help in benchmarking the rough time and cost for designing, developing, testing and launching an enterprise level headless E-commerce site with back end integration to an ERP for Products, pricing, Sales order creation, Order Status, Invoicing & Inventory? Based on rough requirements from my users I quoted 17 months and $1 million.  Am I way off base? 

Based on articles such as https://www.cleveroad.com/blog/ecommerce-website-development-cost/
and
https://www.cloudways.com/blog/ecommerce-website-cost/   

the cost and duration seem reasonable. However, there are many unknowns:
- If the ERP is older or lacks APIs, this could increase development time.
- Customizing the e-commerce platform to meet specific business workflows can add time.
- Building a flexible front end while integrating multiple systems may require extensive testing and development.
- Handling payment gateways, shipping, and tax systems can introduce more complexity.
- Security features (SSL, GDPR, PCI-DSS)  
- Rigorous testing phases (unit, integration, user acceptance) for both the e-commerce and ERP systems. 
- Development costs vary depending on team size, location (in-house vs. outsourced), and the use of specialized contractors.
- Post-launch maintenance (depends on the terms)

Given your information, I would not judge your estimates off base. However, as always, it all depends ... Make sure you have a clear understanding of pricing model and technical interfaces, as these can be dangerous pitfalls.

I agree with David's government variable.  If selling to US federal, allocations to government purchasing requirements should be given priority and built in a away that is repeatable and consistent.  It will pay off in the long term.

Your baseline assessment of 17 months and $1 million without knowing anything else, I would say is likely the minimum, but there are a lot of factors. The main one being API availability from your ERP, Tax System, and any other dependencies you have on order placement.  

Headless gives you great control over your user experience and branding options, but all the data ensuring order success, valid payment, fraud prevention, user account setup, and verification will be coming from another platform. 

ERP resources are always scarce and expensive.  They own and run the core platform your channel is dependent on.  So I recommend bouncing your estimate off that team's service scalability and engineering capacity. 

Necessary eCommerce services to evaluate:
Account
Tax
Shipping
Order Placement (Containers)
Billing
Inventory
Payment Gateway/Fraud Prevention
Analytics

Couple thoughts: 1. Are any of the stakeholders government? If yes, extend the time. 2. Are you using an off the shelf solution? With an ERP you should not need to design/build so much as integrate, deploy and train. 3. did they ask for BI or data analytics? 4. what is the payment/collection system? I'd avoid bolt on solutions and get something that is already proven to work with the ERP with built in APIs if you can. good luck.