In most organizations, especially large ones, one must get a lot of buy-in and this usually involves making a business case, predicting cost savings, efficiencies, potential return on investment, etc., etc., etc., Oh, case studies and benchmarking from other organizations help too. And during these processes remember you are not just the person delivering training, but you must be the training consultant and instructional designer. Identifying training needs, offering the most effective solutions and in some cases identifying human performance issues and strategies to resolve them.
But when I am stuck I have found that creating a prototype helps a lot. Something they can see and try for themselves helps create a lot more buy-in. And if you make the prototype available to an audience of potential users, it can stir up excitement, you may even have a grassroots campaign on your hands. Plus, with a prototype no absolute commitment has been made (you still have time to back out), if there are any expenditures they are much lower, and it gives others a chance to "get on-board," contribute to the design, and rally to the cause.
So, I say "If you get stuck, build a prototype and apologize later."