Subcontractor's Bid Document to GC has "Very Specific Language" that acceptance or awarding of the Bid requires a signed contract between both parties (GC & Sub as named in Bid Document) . Bid is selected and awarded by e-mail by the GC with no acceptance by Subcontractor and Agreement cannot be reached on contract language and/or other contract requirements with "no signed contract existing between GC and Subcontractor". The Project starts with other subcontractors doing their contracted work - am I liable for the work that I bid on with damages to General Contractor because the GC most likely cannot meet their construction schedule with Owner because the GC has to find another subcontractor to do the work that I bid on?
It honestly depends on more of the facts. The language in the bid document is fine. However, if there are any other facts that show that the GC rightfully relied on you to do the work, and you entered into some other agreement (i.e. there is an email out there from someone at Sub where the Sub says "don't worry about that language in the bid documents, we don't need a new contract before performing the work"). Obviously the email in this scenario changes the nature of the bid document, and using the email with the bid document, it looks like a contract. Then if the court finds a contract in that situation, and Sub did not perform the contract, then the court could easily find damages to GC stemming from Sub's breach of the contract.
I would make certain that the facts you stated are the only facts and there is not something else out there that the GC could rely on to make the case that a contract exists.