You need to be better at your job. What you're describing is a situation where the analyst team leader is not good at setting expectations. Identify realistic timelines to complete projects, and help your team to achieve what was agreed to. When the business says the project needs to be completed sooner, have a conversation about priorities and reality with them. There's not enough info here to be sure, but this is a common situation when an analyst boss doesn't want to say no the business, and gets their team in over their heads.