We are sitting on the black leather sofas in a compartment at the rear of the Tory leader's campaign coach – a zone some of his team call David Cameron's "love pod". The destination this sunny Saturday morning is Essex, the county that produced Essex Man, devoted follower of Margaret Thatcher, and some of the iconic victories that punctuated the last period of Conservative rule.

Had things gone to the original campaign plan, the Conservatives would now be leaving 13 long years in opposition and cruising to a parliamentary majority in 12 days' time. How hard could it be to defeat a tired, three-term government led by a very unpopular prime minister with low communication skills who has presided over the worst recession since the 1930s?

Then Nick Clegg happened, the Liberal Democrats erupted. Everyone's assumptions were thrown into the air and the Tory campaign was plunged into a shock that Cameron is good at masking but canot entirely disguise. We put it to the Tory leader that he never expected to be polling in the low 30s with less than a fortnight to go.

"No, of course. No," he concedes immediately. "I never thought it was going to be easy. I've never thought there was some sort of glide path to election success. But the campaign has been shaken up. No doubt about it." But he maintains: "I think it's still quite possible to win. That's what we're shooting for." This is nevertheless quite a recalibration of Tory ambition. A month ago, they assumed a Conservative victory was pretty much inevitable. Now their leader thinks that it is merely "quite possible".

Of the sensational change in fortunes caused by the Lib Dem surge, he says: "The key is: can you change your approach? Can you think on your feet? Can you respond to this?"

The way the Tories are responding is interesting. Rather than direct more resources to try to deal with the yellow peril, they are focusing even more on Labour, believing that the slump in support for Gordon Brown makes Labour seats newly vulnerable to the Conservatives. Cameron says that Labour-held Thurrock – today's venue for a rally – was not on the original list of targets. The game plan now is to try to make additional gains from Labour to compensate for not winning Lib Dem seats they had originally expected to take.

Many Tories privately say that their leader made a colossal strategic error when he gave Nick Clegg the opportunity to shine by agreeing to the televised leaders' debates. If Cameron fails to become prime minister, historians are likely to call it a massive blunder. "I absolutely knew at the time that we were going to give a leg-up to the third party," he says, insisting that he still does not regret the decision because it has been "good for our democracy".

This morning, Cameron has suddenly launched a new idea: a proposal that, if the premiership changes between elections, an election has to be held within six months. That is very clearly targeted at Gordon Brown. It also flags up a Tory fear that Labour could ditch Brown for a new leader in order to facilitate a post-election coalition with the Lib Dems: "You could have someone as prime minister who wasn't even in the televised debates."

His latest proposal would be a major rule change to Britain's democracy, which is, we remind him, parliamentary, not presidential. The policy features nowhere in the Tory manifesto. Isn't it a sign of panic that he is suddenly proposing a major constitutional change?

He bridles a little: "I didn't think there was a law against announcing policies in an election. Normally, you guys are saying, 'Come on, where's the news? Where's the beef?'" He claims it is "a very logical extension" of what his line has been all along: there should have been an election when Brown took over from Tony Blair: "It's just the formalisation of something that I've been saying for some time."

There were changes of prime minister during both world wars: from Asquith to Lloyd George, and from Chamberlain to Churchill. Under his proposal, there would have been snap elections in the middle of these conflicts. The forehead furrows, then he rallies: "This is a proposal for the future, not the past." He adds that "in the modern world people feel rather cheated" if they haven't voted for the prime minister.

At the rally, he delivers his current stump speech, inveighing against the prospect of a hung parliament. This is designed to drive voters to the Tories for fear of "the very real risk we'd be stuck with another five years of Gordon Brown". He also repeats his line that "the world wants to see Britain deal with its debts, get on and make decisions, avoid the jobs tax, get the economy moving. I think all those things are more difficult with a hung parliament. I accept that this is a challenge at the moment, because some people are seeing a hung parliament as a change."

Indeed they are. In some polls, as many as half of voters want to deny unfettered power to any single party. We draw him into some debate about what the Tories would do if no single party had a majority.

"We would behave in a responsible way." What does that mean?

He tries deflecting with a joke: "Obviously, it's pretty clear that we wouldn't prop up a Labour government . You can rule that one out."

What he does not rule out is the possibility of coalition or some sort of other deal with the Lib Dems. He declines several opportunities definitively to say no to it, sensibly hedging his bets in case Clegg does turn out to be the kingmaker. And if the price was swallowing the Tories' hostility to electoral reform? He begins by defending first-past-the-post. "I want us to keep the current system that enables you to throw a government out of office," he says. But if it was the price of getting into power with Lib Dem support, he merely says: "We think this is an important issue."

The Tory leader repeats the official denials that the Conservatives have had anything to do with attempts by some rightwing papers to smear the Lib Dem leader: "I'm not responsible for what the newspapers write. Many believe that the press attacks on Clegg have been counterproductive, offering further examples of the old politics against which people are revolting. We put it to Cameron that the Tory press can be the Tory party's worst enemy. "Exactly."

He reminds us that some of those papers have previously been less than flattering about him. "I've had plenty of battle scars from the Tory press. I've had four-page editorials having a go at me. So before we write all this up as a conspiracy, I think we should have a deep intake of breath."

Early in his leadership, Cameron made a concerted effort to woo liberal Britain. His first newspaper interview as leader was with the Observer, in which he spoke a very different language to his predecessors' about immigration, civil liberties and gay rights. Since then, we put it to him, people initially attracted by that approach have become steadily more sceptical that his party is an appropriate home for their support.

He argues that it still is, and that "the modern liberal Conservative party" should be winning the support of "a liberally minded person who wants to get rid of identity cards, wants to give the environment a proper priority, education comes high up your list, and believes we should have a government that respects civil liberties rather than tramples on them. One of the keys to this election is people who are broadly speaking small 'l' liberal."

Outbursts by prominent Tories – for instance, by his shadow home secretary, Chris Grayling – have fuelled scepticism that the Conservative party is anything like as modernised as the leader protests. "I accept, if you take the issue of gay equality, I completely accept the Conservative party moved too late and too slowly," he says. "All conservative parties across the world have been on a journey and I would argue we've gone a lot farther than others. But do I think we should have gone farther and faster? Yes."

Asked to confirm that Grayling will be home secretary if the Tories win the election, he won't: "I have not given blanket guarantees about jobs."

Another source of unease – shared by some of his own frontbench – is the limited tax break for marriage that will go to just one in three couples and may seem unfair, offensive and discriminatory to single parents, stable families where the parents simply choose not to marry, and to the widowed. How does he explain this policy to someone with a family whose spouse was killed fighting in Afghanistan? "No one is losing out from this tax break."

Yes, they are, because somebody else is getting more.

"Well, you're giving a tax advantage to marriage because marriage is a good institution. There is tax relief in our system for taking a bicycle to work. Are we discriminating against non-bicycle riders?" After this rather bizarre comparison, he gets back on track, arguing that it is "a very progressive policy" because the £3 a week will go only to people on basic rate tax with a low- or non-earning spouse.

He also extols his proposal to remove "the couple penalty" in the tax credit system. "At the moment, if you get your girlfriend pregnant and move in with her, never mind whether you're married or not, you are seriously penalised. I'm changing the system to remove the penalty against couples."

He's also sticking with the pledge to raise the inheritance tax threshold massively: "It was very popular and remains very popular," he says.

He can't, however, guarantee that a Tory government would not raise VAT. "We don't want to. We have no plans to." But… there's a but. "We've never said you can rule out tax increases because it's not a responsible thing to do."

The occupant of the "love pod" is approaching his destination of the rally. If he fails to win the election, will he quit as leader? He doesn't want to go there. But if he wins, he likes to suggest that he wouldn't overstay his welcome. It is "definitely true", he agrees, that both Thatcher and Blair stayed too long. "Do politicians eventually go past their sell-by date? Yes, of course they do. I'm sure that Samantha would whisper in my ear at the appropriate time."

He has to get over the threshold of No 10 to start with. Given that so much seemed to point to a Conservative victory when this campaign began, if he fails to deliver his party will react with something louder than a whisper.