Back in April, Patrick Butler predicted that cuts to in-work benefits would “surprise and frighten Tory voters.” If Thursday’s Question Time is anything to go by, he was right. An angry Conservative voter tore into energy minister Amber Rudd over the government’s planned cuts to tax credits. Her outrage prompted this tweet from a Tory Party member:

I actually feel sick to my stomach to be a member of the Conservative Party tonight over #taxcredits. That lady spoke for millions #bbcqt — Charlie Evans (@Chevans93) October 15, 2015

These are not isolated comments. There is a growing disquiet among Conservatives about the impact of tax credit cuts and the effect they will have on some Tory voters. Conservative supporting journalists have attacked the proposal and the Sun is running a campaign against it.

A poll for Sky News in the summer found that most people didn’t think tax credits counted as welfare. There was much higher support for cutting welfare than for cutting tax credits. Among Tory voters, 77 percent thought welfare should be cut but 50 percent were opposed to cutting tax credits. It is likely, therefore, that some people voted for welfare cuts without realising that they, too, counted as welfare claimants.

In the minds of many people, welfare still means something that only the unemployed get. If ever the stereotype of the work-shy dole scrounger were true, though, it certainly isn’t now. The unemployed are a shrinking proportion of benefit recipients. As this table from the OBR’s most recent Economic and fiscal outlook shows, the big lumps of social security spending are, in rough order, pensions, tax credits, housing benefit, disability benefits and child benefit.

The problem is, David Cameron has ruled out cuts to pensions and child benefit which doesn’t leave much to go at if you want to cut welfare by £12 billion. There is simply no way to do it without taking away in-work benefits.

This gives Tory opponents of tax credit cuts a problem. Their stance is as arithmetically challenged as that of Labour MPs who refuse to oppose the fiscal charter. Eliminating the government deficit by 2019-20, without raising any extra taxes, will need a cut of around £30 billion from public spending. The government is planning a 60:40 split between cuts to public services and welfare, so just under £18 billion off public services and £12 billion off welfare.

If the government can’t cut welfare by £12 billion, it has to increase its public service cuts or abandon its deficit reduction target. Every pound the government fails to take off welfare costs has to be saved from public services, thereby increasing the likelihood of one or more of them collapsing before the end of the decade. Given that tax credits are the largest element of social security apart from the protected pensions, it is almost impossible to eliminate the deficit by 2019-20 without cutting them. Therefore, if you support the government’s deficit reduction target and you don’t want extra tax increases, you must support cuts to tax credits.

Voters have an excuse for not grasping the maths of this. They have other things to worry about. MPs haven’t though. They get regular briefings from the House of Commons Library explaining all this stuff. This is from the January update.

You see those gold bits? Those are tax credits. You can’t touch the dark green bits so tell me where else that £12 billion is going to come from.

It will be interesting to see how the government squares this one. Will it capitulate over tax credits and abandon its deficit target or put up taxes? Or will it hold the line and ride out the storm. Or will it, as I suspect, fudge a bit here and there, while hoping to God that something turns up.