Does a "deep state" exist in Egypt? I've been asking myself that in the streets of Cairo as more and more people – doormen, shopkeepers, policemen's families and taxi drivers – express their support for "Stability Shafik", Hosni Mubarak's last prime minister who watched his former boss jailed for life on Saturday. Ahmed Shafik says he stands for stability. A spot of security on the streets – and now the young people of the 25 January revolution are asking what happened to them. Some of their cartoons are funny. The one where Mubarak's face morphs into Shafik's – via the all-powerful Field Marshal Tantawi – is a cracker. The young sometimes seem to be the only Egyptians leftwith a sense of humour – until you talk to them. And they speak of betrayal.

Is Mubarak's ghost going to be reinstalled, substituting a security state in place of a democracy? That's what many of the protesters are asking in Tahrir Square ahead of the second round of presidential elections on 16 and 17 June.

Shafik has already sectarianised the run-off by saying that his challenger, Mohamed Morsi of the Muslim Brotherhood, would have Egypt's capital in Jerusalem – a clear dig at Morsi's links with Hamas and Israel's fears of an Islamist government, though Shafik might have said Morsi wanted the Egyptian capital in Mecca. That would frighten the Saudis. Under Shafik, the Egyptian capital will remain Cairo. It's all a bit rhetorical. But how did all these Egyptians suddenly come to regard Morsi as a dangerous man? Is the crusty old dictator's security regime still in action? They were, after all, past masters of the fraudulent vote. A little tinkering here and there – especially in the villages of Upper Egypt – and we might see Shafik safely installed.

"Do you think we had a democratic election?" a lady from Al-Watan newspaper asked me in Cairo. "Do you really think so?" She obviously didn't think I did. Then I'm chatting to a very prominent Egyptian reporter and the questions come thick and fast. "Isn't there a 'deep state', can the security apparatus not fix the election by using all their old agents?" And yes, why can't the guys who handled Mubarak's witless polls not put the word out that Morsi is too dangerous to have around.

And then there are the cops who've got away with it; the sniper, for example, who shot demonstrators in the eye and whose picture was actually printed in the Cairo press but who has never been arraigned. Not a single police thug has been charged with attempted murder. I even heard from a reliable source that a policeman imprisoned under the Mubarak regime for brutalising a Cairo man served his sentence and then emerged to be reappointed and promoted. And he's still there. Why has not a single "baltagi" plainclothes criminal been arrested for beating and killing demonstrators?

Then there's the obvious question of who Washington would like to see in power. The brotherhood? Surely not. However democratic he claims to be, Barack Obama doesn't want Morsi installed in Cairo before his own presidential election.

So think of the demonstrators in Cairo who still want their revolution honoured, who believe the Mubarak regime has got off too lightly. New trials for the Mubarak clan? Unlikely, of course. But revolutions don't always pan out quite as we want. Past revolutions come to mind: France and Russia. Revolutionaries are always demanding security against foreign plots. It's all about questions right now. And the Egyptians want to ask them before they get the "security" some people think they deserve.