Bitcoin (and to a lesser extent almost all other cryptocurrencies) is a threat to the current monetary system and to the power this legacy system represents for governments. That could convince some governments to launch attacks on the Bitcoin network to try to interrupt or disable it. Bitcoin has demonstrated its resilience against many attacks already and we will now have a look at some ways governments could try to disable it and how Bitcoin will defend itself (We are choosing Bitcoin instead of "a public chain" for making the argumentation clearer.)
The most probable attacks from governments against Bitcoin would be based on regulation. We divide those attacks into three categories: forbid the underlying cryptocurrency, forbid companies providing services related to Bitcoin, forbid the installation and use of nodes and wallets. Firstly, a government could forbid the exchange and use of a cryptocurrency. If nobody were to trust or use that cryptocurrency anymore, that would remove the incentive to maintain the blockchain and that blockchain will stop being supported. But by making it illegal to use a cryptocurrency would not stop its use. It is illegal to transact in US dollars in Venezuela but that does not prevent the dollar to be the most used currency there. Secondly, the government can forbid companies to provide Bitcoin services. But there is a vibrant community of developers who write opensource code and services and find other incentives than profit and salaries to develop services. Lastly forbidding the installation and use of nodes would not efficiently prevent anybody to download and use them, as shown by the example of piracy in the music industry. It is also important to note that if only one or a few governments would impose restrictive regulation on Bitcoin, it would still be easily used in other countries and that would create regulation arbitrage and potential emigration. And those restrictive regulations would also undermine the innovation and future economy in that country if we consider that blockchain technologies will be an important part of the economy in the future.
One or multiple governments could stop net neutrality, limit internet access and/or block certain IP addresses based on their involvement in the blockchain network. The response from the users of the network will be to use IP obfuscation tools like VPNs, TOR or I2P.
Another attack from governments could be social attacks like misinformation. Those attacks have been happening for many years now, associating in the mainstream media Bitcoin to criminal activities. They might have had some negative impact, but those impacts are only temporary as more and more people understand now that criminal activity is only a small part of what Bitcoin allows and will allow in the future.
The last attacks we will consider are 51% attacks and quantum attacks. Let us start with 51% attacks with classical computers. The attacking government would need to gather an enormous amount of computing resources to be able to launch such an attack. And while attacking, it will need to spend an enourmous amount of energy. If it can succeed in mining around six blocks in a row, it could make some big double spends. But those double spends will not greatly undermine the confidence in the network. To significantly undermine that confidence, it would need to rewrite history and be able to calculate the POW of many blocks. The amount of resources required for that is so huge that it is considered impossible for any single party, even with large financial resources. This would be different with quantum computers. Quantum computers could have a certain advantage with the current POW algorithm, but it has been estimated that those computers will not be ready to take advantage of that before 2040 (Quantum attacks on Bitcoin, and how to protect against them), and it would be possible to modify the POW algorithm to limit that advantage. The main threat from quantum computers, however, is the attacks on the private/public key cryptography used in Bitcoin (see previous link). The threat could arrive in around 7 years, but there are countermeasures being worked on and explained in the referenced article.
The risk is not zero that any of those attacks, or new ones, can have significant negative impacts on Bitcoin, but Bitcoin has shown and strengthened its resilience with every previous attacks. We are convinced it will continue to do so and resist any attempt to disable it. On the resilience aspect of Bitcoin, we cannot resist encouraging you to watch Andreas Antonopoulos' talk "Bitcoin, the Bubble Boy, and the Sewer Rat".