Many of the miners have, in fact, favoured the so-called Bitcoin Unlimited solution.
They said that allowing them to increase the 1MB block size would speed up transactions and reduce transactions fees.
But this could also make mining more expensive, and impractical for small "mom and pop" operations, leaving it under the control of a handful of large corporations.
That is because more processing power would be needed to verify transactions.
Furthermore, additional data bandwidth and storage space would be needed to transmit and store the blockchain, since it would become much bigger.
Critics also say the move would make Bitcoin more vulnerable to hackers.
Moreover, some people are concerned that giving the miners power to vary the block size might undermine the principle of Bitcoin being decentralised, with no equivalent to a central bank running the show.
It appears so.
A middle-ground solution - called Segwit2x - aims to start sending signature data separately from the blockchain later this week and then to double the block size limit to 2MB in three months' time.
An initiative called Bitcoin Improvement Proposal 91 (BIP 91) states that if 80% of the mining effort adopts the new blockchain software involved and uses it consistently between 21 July and 31 July, then the wider community should accept this as the solution.
The good news for those who like the idea is that close to 90% of miners appear to back the effort, according to Coin Dance, a Bitcoin-related statistics site, external.
Other plans exist to try again after August if the target is missed.
But a risk remains that if use of Segwit2x software never reaches the required threshold or that hardcore opponents refuse to buckle, then it could result in two different versions of the blockchain, and in effect two types of Bitcoin.
Such as schism could help rival cryptocurrencies, such as Ethereum, prosper and ultimately doom Bitcoin altogether.
One expert, however, said he believed that was an unlikely outcome.
"The vast majority of people in the Bitcoin community are opposed to splitting Bitcoin into two competing cryptocurrencies," said Dr Garrick Hileman, research fellow at the Cambridge Centre for Alternative Finance.
"Such a move would weaken Bitcoin's network effect advantage and sow confusion.
"It is much more likely that people who are dissatisfied with Bitcoin's direction will simply move on to something else, which is what we've seen in the past."
"More and more small to medium sized companies who are 'mining' at the moment will be taken out of the game if they won't adapt and grow," said Martin Sims, CEO of Coin Geek., external
"It's a very competitive industry and everyone needs to update and evolve as the popularity of bitcoin increases and the game changes."