How does the Conservative party want Theresa May to respond to the suspected chemical weapon attack in Syria? A quick browse of the papers, news channels and social media this week would suggest that the Tories are urging a meek and indecisive prime minister to transform into an iron lady and take drastic action.

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Johnny Mercer – Tory MP and former soldier – used a widely praised Telegraph article to call on the prime minister to put an end to “pious politics and endless self-flagellating” and bypass a parliamentary vote on the issue. Tom Tugendhat – the Conservative chair of the foreign affairs select committee – has said that “standing aside while people are gassed or sharing the murderer’s lies doesn’t make us safer”. Even May’s nemesis George Osborne seems to be on side – using a leader in the paper he edits to argue that there is no need for a Commons vote before action in Syria.

As British submarines complete with Tomahawk cruise missiles are ordered to move within range of Syria, it looks as though May is steeling herself to take their advice. The prime minister has summoned her cabinet for an emergency meeting this afternoon to discuss whether Britain should join its French and American allies in proposed military strikes. The signs so far suggest that this discussion won’t be extended to MPs en masse, with figures in Downing Street keen to stress there is only “limited precedent” for parliament to be consulted.

But it would be a mistake to assume this means May has her party’s full backing. Scratch the surface and it soon becomes clear the Conservative party is nearly as divided as Labour on the issue. The only difference between the divisions within the Labour party and the Tories on intervention in Syria is that the Conservatives’ are better hidden.

While the vast majority of Tories would happily condemn Bashar al-Assad for the attack, the disagreement begins when it comes to what the response should be. For all the noise this week, there is a sizeable group of people who are still stung by the events surrounding Libya and Iraq and remain cautious over the benefits of intervention. They see the language of younger, more boisterous MPs as verging on reckless. More than one minister can be found who’ll warn that the approach of Mercer and Tugendhat would lead to a third world war. This group argue: if there’s no grand plan for regime change, why fire just to forget?

It doesn’t help that Donald Trump is flirting with war via Twitter

Even some MPs who voted with David Cameron in 2013 – when the then prime minister lost a Commons vote on military action against Assad by 13 votes – wonder if it’s a worthwhile venture. Five years on, it’s not clear what options to intervene in Syria are left. Julian Lewis – the chair of the defence select committee – warned this week that a military campaign against the Syrian president could mean the UK government is inadvertently helping al-Qaida.

It doesn’t help that Donald Trump is flirting with war via Twitter. Cautious Conservatives question whether it is such a good diplomatic idea to rush to the side of a man tweeting “Get ready Russia” and boasting about “smart!” missiles. “If it were any other US president maybe it would be a different reaction,” explains one such MP. The heightening of tensions between the west and Russia means that any “measured response” will also be a political one.

Finally, there are those MPs who agree with the idea of intervention but value the sovereignty of parliament. This group would feel uncomfortable if such a big decision was taken without consultation. Were May to ignore them, it would hurt party morale and make her day-to-day job of governing with no majority harder.

But the problem is if the decision were to go to parliament, it’s not a sure thing that May would win. She would almost certainly have to rely on Labour rebels’ votes for her majority in this instance. Some in government think the risk of asking for approval is too great to be worth the gamble. Were she to lose a vote, it would be a devastating blow to her standing on the international stage. After all, nothing says “global Britain” less than a prime minister who can’t do as she wishes on foreign policy.

The longer the clock ticks, the more difficult things become. Had action been taken on Monday with parliament still in the midst of recess, May would have found it easier to get away with a retrospective vote on her actions. That is a more difficult sell now. As speculation grows on the size of the response and its aims, the number of questions over the UK’s participation grows. It’s not just her MPs who may see red. A Times/YouGov poll today on the public’s appetite for military intervention serves as a stark warning of problems ahead – just 22% of the public backs airstrikes on Syria while another 34% “don’t know”. If May goes ahead with strikes, she will need all the help she can get from her party in winning the “don’t knows” round to her cause. The problem is that whatever the prime minister does, she will alienate some of the colleagues she must depend on.

• Katy Balls is the Spectator’s political correspondent