I have two managers, and each says their deadline comes first

I report to a department manager and a project manager.

On the organization chart, the arrangement looks collaborative. In practice, I receive two lists of priorities from people who each believe they have final authority over my week.

On Monday, my department manager asked me to finish a staffing analysis by Thursday. She said it was the most important item because leadership would use it on Friday. On Tuesday, the project manager moved a client presentation forward and told me to spend the rest of the week rebuilding the data.

I showed him the staffing deadline. He said, “You’ll need to work that out with her.”

When I went back to her, she said the client project could not repeatedly displace department commitments. She did not change the deadline. Both conversations ended with someone explaining why their work mattered and nobody deciding what would not happen.

I can usually rescue the collision by working later. That has made the structure appear functional. Each manager sees their deliverable arrive and assumes I successfully balanced the priorities. Neither sees the evening where both were completed.

Last month, I tried sending a joint message: two deliverables, estimated effort, and a request for one shared decision. The department manager replied first and chose the staffing work. The project manager called me privately and said I had escalated unnecessarily.

I do not want to copy both managers on every scheduling question. I also cannot remain the private negotiation channel between them. A dual-reporting structure should create broader support, not require the employee with the least authority to settle conflicts between leaders.

I am considering a weekly fifteen-minute priority check with both managers and one visible list showing capacity, deadlines, and the person who approved any change. For midweek conflicts, the manager introducing the new urgent work would need to bring the tradeoff to the other manager rather than send me back alone.

Would that create useful clarity or turn every week into a miniature governance meeting? How do you work under two managers without becoming responsible for resolving the authority they share on paper but avoid using together?