Philip Hammond began this week as “spreadsheet Phil” – the steady-as-she-goes chancellor ready to steer HMS Britain safely through Brexit – and ended it as the author of the “omNICshambles”.

Colleagues who know him well said it was precisely because he likes to dive into the numbers that he had taken such a pasting in the press for what the Sun described as a “strivers’ tax”.

“Philip’s amazing when it comes to the detail; but on things like this, people aren’t interested in the detail, they’re interested in the headlines,” said one.

Allies insisted the chancellor was in relaxed mood ahead of the weekend – he’s not climbing the political ladder or chasing one day’s headlines they argue; he is trying to make the tax system fairer and that’s what this week was all about, they said. Job done.

Except, on Thursday night, Theresa May felt forced to devote a significant chunk of a Brussels press conference that was meant to be about UK-EU relations to defending her chancellor’s budget, and its controversial national insurance rise for self-employed people.

Her robust defence of the policy, which she said would make the tax system fairer and more progressive was undoubtedly helpful. But no chancellor wants the prime minister to have to come out swinging for them – and May’s agreement not to legislate until the autumn was a clear admission that the government could not have got the measure through parliament at this time.

As a result, on Friday fewer rebels were willing to go public with their disapproval of the policy, placated by the pledge of “consultation”. Yet, several told the Guardian they don’t expect the measure to reach the statute book unscathed.

Hammond never sought to disguise the fact that his first budget would be light on measures. It was designed as a holding operation, the sort of package chancellors usually deliver before general elections just to keep things ticking over.

The reason was simple: Hammond is moving the budget from the spring to the autumn and wanted to save up the fireworks for later in the year. As a result, there was quite deliberately no attempt at replicating the political theatre so beloved of George Osborne or Gordon Brown.

Hammond compensated by showing an unexpectedly light touch and his jokes – both at his own and Labour’s expense – went down well in the Commons at the time.

However, that meant the NICs rise was the only announcement on Wednesday worthy of note – and that proved to be the budget’s Achilles heel. Normally, chancellors can hide pieces of bad news by announcing a number of voter-friendly measures they know the media will highlight. This time there was nothing other than NICs to write about, and that meant the budget was not the boring affair Hammond thought it was going to be.

The next day, he won support from the tax experts at the Institute for Fiscal Studies. In their time, both Brown and Osborne found their budgets being picked to pieces by the IFS, but Hammond got a relatively easy ride.

Paul Johnson, the IFS’s director, said it made perfectly good sense to start to bring NICs for the self-employed into line with those for the employed, adding that the impact of the measure would be dwarfed by welfare cuts announced by Osborne after the 2015 election. “This appears to break a foolish manifesto commitment not to raise any of the major taxes. On the other hand it is a small change taking a small step to correcting a big problem with the current tax system,” said the IFS.

It was not, however, enough. This was one of the times when economics mattered less than the politics. While Johnson’s researchers were running through the distributional impact of the budget, a revolt against the NICs increase was gathering momentum at Westminster.

Iain Duncan Smith, John Redwood and a stream of other senior Conservatives, including a junior minister, Guto Bebb, spoke out against the measure, and it became increasingly clear to government whips that at best they would have to agree to kick it into the long grass.

Hammond has been a friend of May’s for many years – but he is not an integral part of her political project, as Osborne was for David Cameron, or Brown for Tony Blair. He does not attend the 8.30am meetings at which the day’s agenda is set and political problems are chewed over.

One government source described the past week as a “black mark” against a chancellor suspected by the most ardent Brexiters of harbouring a secret desire to thwart Britain’s exit from the EU.

And apart from the fact that spreadsheets only get you so far in politics, some in Westminster drew another lesson from the past few days: that even with Labour trailing the Tories by 19 points in the polls, May’s government has less room for manoeuvre than it might sometimes appear. With a working majority of just 17, small but noisy groups of renegade MPs are able to exact climbdowns.

As one exasperated Tory moderate, who backed Hammond’s approach if not his messaging, put it on Friday: “It’s concession politics.”