After seeing his proposal to cut tax credits defeated in the House of Lords on Monday, Britain’s chancellor, George Osborne, promised to “lessen” the impact of the changes.

But he also vowed, in a speech to the House of Commons on Tuesday, to press on with reforms that are meant to save the government around £4 billion in annual spending.

In an usual demonstration of its power, Britain’s unelected upper chamber sent the legislation back to the Commons Monday night in a move that Osborne said raised “constitutional issues that need to be dealt with.”

The government accused the Lords of breaking a century-old convention under which it does not block financial legislation that has the support of the House of Commons.

But the Labour and Liberal Democrat peers, who can outvote the Conservatives in the upper house, argued that the measure to cut tax credits wasn’t technically introduced as part of a money bill. Hence, they said, the convention did not apply.

A growing number of Conservatives is now unhappy about the reforms as well.

Tax credits were introduced by the last Labour government. Osborne has proposed to reduce the threshold at which the credits kick in. According to independent research, this could leave low-income families up to £1,000 per year worse off.

Osborne insists that raising the income tax threshold as well as the minimum wage and extending free child care will make up the difference.

Whatever the merits of the legislation, Monday’s vote has raised a more serious issue for the right-wing government. The Conservatives have long opposed turning the House of Lords into an elected senate but if the left-wing majority there continues to resist legislation, the ruling party may be tempted to revisit its position.

Prime Minister David Cameron could bypass the opposition by stacking the upper house with loyalists. He can appoint as many peers as he wants.

But the sudden appointment of the more than 150 new members the Conservatives need for a majority — in what is already the world’s largest legislative body — would surely call into question the Lords’ legitimacy again.

Fraser Nelson argues at The Spectator that it is not worth the fight. “What does it say about Tory values?” he wonders.

That the party will make a constitutional crisis out of its desire to tear away financial support from low-paid families who had thought that the Tories were on their side?

Better for Osborne — the architect of turning the Conservatives into Britain’s “workers’ party” — to step back and find the necessary savings elsewhere.