The less time you have left, the less valuable you are to a new employer. Hiring someone who can work for 6 years makes sense. Hiring someone who must leave in 18 months is much more of a risk. Therefore you are at an increasing disadvantage in any negotiation where your best alternative to agreement is to seek alternative employment, e.g. Salary increases, change of project.
You're right about the green card, however even if you can get the employer support you need, it takes years and further restricts your employment options in the meantime.
If you're on a H1B visa, you really need to figure out a plan to a Green Card ASAP, unless you're not planning to stay long term.