Any of the concerned “alarm clock” Britons listening to the Deputy Prime Minister this morning may well have felt comfort at the announcement of a £700 tax cut by the end of Parliament.

In Nick Clegg’s own words on the Today programme: “We are going to put £200 back in the pocket of every single basic rate taxpayer from 5 April onwards, and by the end of this Parliament it will be £700, as we move towards this central pledge of making sure that no one pays any income tax on the first £10,000 they earn.”

Hurrah! the legions of alarm-clockists cried into their Corn Flakes, except it’s not quite as easy as that.

The first bit of that sentence is fine, it arises from a rise in the personal allowance announced in the Budget to £7,475, which will cost about £4bn per year. The second “by the end of this Parliament it will be £700″ is a massive multi-billion tax cut which is uncosted in the public finances.

The cost of this move? £11.5 billion per year by 2015. Uncosted in our public finances, but which Nick Clegg wants to take credit for in New Year interviews.

And you can add that to the deficit. Government ministers would rightly ridicule Alan Johnson for doing the same, I can’t understand the acceptance of this.

It is true that the Coalition Agreement mentions the £10,000 figure, but only as a “longer term policy objective”. The Treasury confirmed to me today that only the first £200 had been costed in the public finances.

I am also rather bemused around the claims about this £200 tax cut. It is almost as egregious as the worst abuses of Gordon Brown’s abacus. Brown claimed to have cut basic rate income tax in 2007 to 20p, when actually almost no-one benefitted because it was entirely paid for by doubling (not abolishing) the 10p rate. It was a tax reform not a tax cut. And most economics journalists heaped scorn on him.

Likewise, boasting about a £200 tax cut costing £4billion a year when you have paid for it by increasing VAT on most of the same people by up to £13 billion a year seems a little absurd. 23 million basic rate taxpayers will clearly pay far far more in extra VAT than they will gain from the £1,000 increase in the income tax threshold. At the very least this is tax reform, not tax cut.

Brutally put, Nick Clegg appears to have forgotten that alarm clock Britons will still be paying more for VAT on their timepieces.

And there’s one other more speculative factor too. If the DPM didn’t just mis-speak about the certainty of the £10,000 move, then in order to keep the policy affordable, the benefit will have to be “neutralised” for higher rate taxpayers. This year it will be achieved by a real terms lowering of the 40p threshold too. This pushes more people in to higher rate tax, and crucially means more people losing their child benefit. If this year’s approach was repeated the threshold for losing your child benefit could be pushed down to £39,000-ish, and see hundreds of thousands more losing thousands of pounds.

And, of course, I have not even mentioned that it is specifically this threshold-raising policy that drives some of the more unpalatable (for Lib Dems) results of the winners and losers tables, so beloved by Nick Clegg. (And, amusingly, the Conservative election unit issued a four page rebuttal of this policy partly for this reason).

So, in his attempt to appeal to our alarm clock instincts, the DPM either mis-spoke, or he told the truth, in which case he appears to have substantially widened the deficit.

Perhaps he is relying on us all being on snooze.