Pro has failed to present a satisfactory case for there being an objective "should". He hasn't even addressed the issue, and thus as he makes each argument he is building a house with no foundation or even a ground to build it on.
I will now quote and then refute the key flaws in Pro's second argument.
The standard for democracy has indeed debated over both many times.
There is nothing in how you framed this debate to suggest that our arguments should be restricted to the standards of democratic countries. The title of the debate merely says "governments" which one can only take to mean governments in general. "Governments" will no doubt have disagreements on how to handle various scenarios. Pro has not clarified why those laws or standards are any more valid than any others when it comes to deciding what the government "should" do.
The Freedom of Information Act
There is nothing in how you framed this debate to suggest that we would be defaulting to US law. "Governments" can also include China and NK etc. and they don't have the Freedom of Information Act. Also, the existence of the Freedom of Information Act proves nothing when it comes whether or not a "should" claim can even be proven. If it can't be proven, and there is no objective "should" then you lose by default. Pro has not clarified why US laws or standards are any more valid than any others when it comes to deciding what the government "should" do, or why "the" government is the US government by default when the debate proposition refers to "governments" in general.
It is hardly "national security" especially if an outside force is going to end the world, and is extremely difficult to prevent.
There is nothing in how you framed this debate that excludes scenarios in which keeping it a secret would be justifiable for national security reasons. You are simply focusing on certain examples and not on others, when other hypotheticals in which it would be justifiable in the context of such a legal/moral standard are equally valid. How then can you make the blanket claim that the government should declare the news in all cases even if I were to pretend that the specific laws or morals you are using are objectively "right" and can lead to an objective "should" which applies to "governments" in general?
The BoP is on Pro to prove there are no examples in which secrecy would be necessary for National Security according to his arbitrarily selected standards which are irrelevant to begin with because he has not fulfilled his most basic BoP of justifying his assertion that there is an objective "should" and it can be proven.
Again Pro arbitrarily defaults to the US. What about other countries and/or time periods in which a hypothetical 30 day apocalypse count down might occur wherein it may be much more plausible? The BoP is also on pro to prove there are no countries/scenarios in which covering an apocalypse up would be more plausible than in the US, since he seems to think the US government can be used as the universal model of "governments" and conveniently leaves out hypotheticals (which the BoP is on him to prove the non-existence of) in which covering up the apocalypse might be plausible or justifiable based on his arbitrarily selected standards.
My case still stands: whether they should or should not does not merely depend on their own moral beliefs, as the whole world must cooperate in order to help combat and alleviate the problems.
Your case does not stand. What about a scenario in which nothing can be done to stop it to begin with? What about a scenario in which conflict or lack of cooperation between governments is the cause of the apocalypse and/or is not something that can be plausibly overcame? Why does any "moral belief" have more weight than any other when it comes to what "should" happen?
Con must also show that it is more moral to keep it a secret.
I have no such obligation. Your BoP demands that you prove that there is an objective, universal "should" and that "governments" in general "should" reveal that an apocalypse is happening to the public in all cases. All I need to do is argue that the debate proposition is wrong, not prove that governments "should" do the opposite. By denying the existence of objective "shouldness" and stating my case that it does not exist, I am attacking you at the root rather than engaging in some unnecessary moral argument that would only be relevant after you prove that there is objective morality or an objective should.
He undermines his own side by appealing to ignorance; just because you are uncertain what to do, does that mean doing nothing is the best course of action?
I have made no such arguments and have in no way undermined my own side.