He has built an unlikely political career on the bold premise that opponents of tax-cutting Republicanism are a bunch of limp-wristed “girlie men” and Arnold Schwarzenegger is nothing if not consistent in his line of attack.

The Governor of California has written yet another chapter in his colourful personal history by sending his leading Democratic rival a metal sculpture of a pair of bull’s testicles.

Darrell Steinberg, the President of the State Senate, is said to have received the rugby ball-sized artwork last week, as lawmakers weighed up how to cope with a budget crisis that has left California $25bn (£15bn) in the red.

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It was accompanied by a handwritten note, suggesting that Mr Steinberg and his left-wing colleagues grow some cojones and make tough choices to cut public spending, which Mr Schwarzenegger deems necessary to stave off the imminent bankruptcy of America’s most populous state.

Sources close to both men told the Los Angeles Times that the gift was a response to a similar gag by Mr Steinberg, who recently sent a package of mushrooms to the Governor’s office, after Mr Schwarzenegger had branded Democratic proposals to raise taxes “hallucinatory”.

Yet the gift was not received well. Mr Steinberg returned the sculpture to its sender with a stern note about the need to protect society’s most vulnerable from cuts in services.

The sudden sense of humour failure appears to represent a calculated attempt to strike a chord with voters who are beginning to lose patience with the inability of successive administrations to balance the books in what is traditionally one of the most prosperous corners of the wealthiest nation on Earth.

California’s government has for years been spending more than it can raise in taxes. The Democrats have a slim Senate majority, allowing them to block most proposed spending cuts, but have found it virtually impossible to raise the money coming into the coffers because Californian law requires two-thirds of lawmakers to endorse tax increases.

The result has been political paralysis. Tens of thousands of public sector workers, including vast numbers of teachers, are now facing redundancy, and many State employees are currently being forced to take an unpaid day’s leave each fortnight.

If coffers run dry, as predicted, next month, California will be forced to start paying bills in “registered warrants”, a glorified IOU note. And with that sobering thought in mind, both parties were reluctant to discuss the exchange of gifts yesterday and appeared to be seriously upset that the global news media had found out about their displays of humorous machismo.

“We never talk about the Governor’s private gifts,” said a spokesman for Mr Schwarzenegger. “Senator Steinberg sent the Governor a gift and the Governor responded in kind. They maintain a great relationship and will work together to fix the budget.”

Mr Steinberg’s spokesman meanwhile denied that he was upset about the practical joke, adding sternly: “We’ve got more important things on our plate right now.”