If you want to get an idea of what Junichiro Koizumi's party thinks of him, just listen to the language used by some of the most influential LDP godfathers.
Last week his main rival, Shizuka Kamei, who heads an influential LDP faction, compared the Japanese prime minister to Adolf Hitler.
And one of the party's most senior figures, 77-year-old Hiromu Nonaka, said he wanted to devote all his remaining energy to throwing out the Koizumi administration.
Conservatives in the party are outraged by Mr Koizumi's reformist agenda and his refusal to spend his way out of recession, hurting vested interests like the construction industry.
Mr Koizumi's popular appeal may be the LDP's most important asset
And they dislike Mr Koizumi's independence in choosing his own cabinet members. For example, he has said he is determined to keep the reformist Economic Minister Heizo Takanaka, hated by LDP stalwarts, in his post.
Yet Mr Koizumi, who has no faction of his own, is almost certain to be re-elected party leader in a vote on 20 September, and thereby retain the Prime Ministership.
Why? The answer is obvious every time you see Mr Koizumi alongside his three rivals for the party presidency.
While they stand stiffly in anonymous dark suits, looking like any other Japanese bureaucrat, he bounds towards the crowds, waving and smiling.
Close up, Mr Koizumi exudes a charisma, confidence and informality unheard of in Japanese politicians.
Shizuka Kamei, 66: former LDP policy chief; favours revising pacifist constitution and more public spending
Masahiko Komura, 61: former foreign minister; wants less austere fiscal stance
Takao Fujii, 60: former transport minister; wants more public spending, but with better focus
And while the public is sceptical about his achievements since he came to office two and a half years ago, promising dramatic reform, he is praised for his style and rock-star looks.
In a country where celebrity is worshipped every bit as much as in the United States, those are impressive assets.
His opinion poll ratings are consistently much higher than those of his party. And he leaves his rivals for dust. In a recent poll of LDP supporters, 77% backed Mr Koizumi, while only 4% backed Shizuka Kamei.
However much they dislike his political style and policies, LDP traditionalists need Mr Koizumi to win the next election.
In truth, Mr Koizumi has proved much less of a reformer than he claimed.
He has bowed to pressure from within the party and exceeded his $250bn cap on government borrowing. This year it will reach US$300bn, although his rivals think the government should borrow even more to revitalise the economy.
He has also watered down proposals to shake up the banking industry. Earlier this year the government chose to nationalise Resona, the fifth largest bank, at a cost of $17bn.
Reformers believe bankrupt banks and corporations should be broken up or sold, allowing healthy companies to do the job of reviving the economy, not the government. They are disappointed with Mr Koizumi.
But he has two achievements which have enhanced his standing with the public.
One is that his balancing-act between reformers and conservatives does appear to be producing results.
Official statistics this month showed the economy growing at an annual rate of nearly 4% - faster even than the US. The stock market has risen more than 40% over the past six months.
It is too soon to say whether this really is the long-awaited Japanese recovery - there have been false dawns before. But economic sentiment is more optimistic than it has been for many years.
His other achievement is that, in part, Mr Koizumi has made good on his promise to reform the LDP, though perhaps as much by accident as by design.
Demoralised by 13 years of economic stagnation, the faction leaders, who at one time determined the choice of Prime Minister and cabinet in back-room meetings, no longer wield such influence.
The largest, the Hashimoto faction, is split this time, with one half supporting Mr Koizumi, the other half backing a rival.
In a country disillusioned by the failings of traditional party politics, Mr Koizumi's personal popularity is a vital vote-winner - and that knowledge makes him more independent of his party than any of his predecessors.
If he does win the leadership race, Mr Koizumi is likely to call a general election quickly, probably in November.
With the LDP facing a stronger opposition challenge from the recently merged Democratic and Liberal parties, that vote will provide the real test of Mr Koizumi's standing with the general public.