can you legally be terminated for refusing to sign an "exclusive right to represent" document?

three weeks ago I was terminated from my job as a sub-contractor working on a PA state project. The project and many others are currently up for re-bid under one large state request for proposal. The prime contracting company informed me three weeks prior to my termination that I would be "moved off the project" if I refused to sign it. I refused to sign the document because of the word "exclusive", explaining the fact that I'm a lifelong resident of the area and didn't want to pen myself in like that. Three weeks later I was terminated, although the official reason given was "budget cuts".

Is there any type of recourse in this instance?
thank you very much for your time.

This is the document language:

Right to Represent Acknowledgement

By signing below, I acknowledge and agree that xxxxx Consulting LLP has the exclusive right to represent me, as a subcontractor of xxxxxx Consulting LLP, to the Commonwealth of Pennsylvania in all matters of and relating to work assignment and performance relating to the Commonwealth of Pennsylvania, Department of Public Welfare Application and Technical Support Services Request for Proposal #RFPxx-xx, throughout the procurement process for such RFP and for the term of any prime contract that may result from such procurement, including any extensions, for the type of positions identified below. This Right to Represent Acknowledgement shall be in addition to any other applicable agreements with xxxxx Consulting LLP.