What counts as transactions fee in Coase Theorem? Coase Theorem says that if the transaction fee is negligible then we will have an efficient allocation of resources.

In some of the samples, they quote that it doesn't matter who has the right to pollute. If people own the river, they will sue polluters and get money. If the polluters own the river, the people will pay the polluters to stop polluting.

It seems that the Coase Theorem presume that if a deal can be made, it will be made.

What about if both the polluters and the river owners (the people) can be better off by striking some deals but they don't make deals because they wait till better deals come along.

Say the river owners want more money for pollution?

Can I say that the transaction costs go up?

Notice that once they agree they can just pay with a credit card and hence there is no transaction fee. However, they play a game of chicken first or whatever to get deals coming up.

Does that mean transaction costs go up and hence, Coase Theorem fails?
Transaction costs (or fees, though I have always heard it as costs) is anything that complicates or prevents a transaction. This includes the example you are suggesting, but also things like the costs of suing, or if many people own the river and it is hard for them to organize and strike a deal. Maybe the legal system is terrible and people break deals all the time with impunity, etc, etc. 

What you want to say in such cases is that transaction costs are high. Only if something changes that make it harder to strike a deal, it would be appropriate to say that transaction costs increase.