Does bitcoin have the potential to be subject to a hard fork where miners are forced to choose which fork they will accept, like Etherum? Some background (Taken from Quartz):


  Ethereum is similar to bitcoin, but it also supports smart contracts,
  agreements written in computer code that execute automatically when
  conditions are met.
  
  Distributed Autonomous Organization (DAO) sought to build a humanless
  venture capital firm that would allow the investors to make all the
  decisions through smart contracts. It was one of the biggest
  crowdfunding effort in history. For Ethereum, the backbone of the
  project, it was a major vote of confidence in its nascent technology.
  
  Then it got hacked, when someone started siphoning money out of the
  DAO. By the end, the hacker, who has said that he was simply taking
  advantage of a technical loophole in the DAO, had amassed $50 million
  in ether, based on current exchange rates at the time. While the core
  developers who designed and run Ethereum didn’t really have anything
  to do with the DAO, they were left to deal with the mess, so they
  decided to hack the hacker.
  
  They managed to stop the theft and move the funds into another smart
  contract where they currently sit: a temporary fix. The way the code
  of DAO was written, there is a question of whether the original hacker
  can still lay claim to the funds. Fixing this would require more
  intervention from the core developers.
  
  Whether to do so has created an existential question for Ethereum. One
  of its underlying tenets is that it’s a decentralized platform,
  meaning the power lies almost exclusively with all of its users. By
  stepping in to fix this problem, it would completely undermine that
  objective. This has led to a heated debate between those who want to
  return the funds and others who say that the the power of smart
  contracts lies in their immutability.
  
  Doing so would basically eliminate the DAO, and move all the money
  into a smart contract that can only reimburse investors. The initial
  proposal was a soft fork where a majority of the Ethereum miners could
  voting on the roll back. Unfortunately, a security flaw was found in
  the voting process, which eliminated this option.
  
  That leaves a hard fork, where the core developers of Ethereum
  unilaterally make the decision to essentially create a new version of
  the network with different rules than the original. Then, miners,
  exchanges, and other major apps that are built on it need to decide if
  they want to a part of the new version of Ethereum or the original.
Yes, Bitcoin could also be subjected to a hardfork. In fact, there are members of the Bitcoin community that feel so strongly that the blocksize should be increased that they are proposing to do just that:
They are working on a version of Bitcoin that is incompatible in regard to the current consensus rules of Bitcoin forcing a permanent split of the blockchain into two. They surmise that their vision for Bitcoin will have greater support than the road map followed by the Bitcoin Core developers and expect to oust the original chain completely.

As they (IMHO) appear to overestimate the support for their project, I don't expect the latter to come to pass.

As Mindwin has pointed out in the comment rightly so, the Bitcoin blockchain has actually forked before by accident: See march-2013-fork, or Bitcoin Magazine's report.
There have also been previous forking attempts, such as the ones pushed for by Bitcoin-XT and Bitcoin Classic.