Have the Republicans come to their senses at last, and put the Tea Party in its place? Read the headlines and listen to the talking heads last week and you'd be tempted to believe it. But, I would counsel, not so fast.

This is primary season here, when each party's voters choose their candidate to fight the general election in November – in this case the 2014 mid-terms. Once upon a time primaries, especially when an incumbent was seeking re-election, were of minimal interest, and more often than not uncontested. If it ain't broke don't fix it, was the prevailing philosophy.

But the advent of the Tea Party, soon after President Obama came to office, changed all that. It was an insurgent grassroots Republican movement, not beholden to the party's great and good, born of loathing of big government in general and of Obama's healthcare reforms in particular. If the Grand Old Party's longstanding representatives in Washington didn't have the spine to change things, then the Tea Party would find people who did.

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And so Republican senators and congressmen deemed wanting in this regard – so-called Rinos or "Republicans In Name Only" – found themselves under attack from their own. One big name after another was defeated in primaries, when only the most ideologically driven activists tend to vote. There was just one problem: some of the Tea Party-driven candidates who did prevail were too extreme or just too wacky to win the general election. In the Senate, seats that Republicans should have held or won were instead gifted to the Democrats.

But now the GOP establishment is fighting back, and last week came their biggest success yet, in the Senate primary in North Carolina, where November's general election could decide whether Republicans recapture the Senate or, for the third time running, see the prize slip through their fingers. They need a net gain of six in the 100-seat chamber, and North Carolina is at the very top of their target list.

Carried by Obama in 2008 but by Mitt Romney in 2012, it's a classic swing state. The incumbent Kay Fagan is a first-term Democrat, competent but vulnerable in a year when Obama is unpopular and when a second-term president's party usually does badly. Her chances would be enormously improved if Republicans picked an unelectable zealot to oppose her.

That, however, the GOP establishment was determined to prevent. It threw its weight – and its money – behind the "safe" candidate Thom Tillis, the vastly experienced speaker of the state legislature. His backers included the US Chamber of Commerce and the American Crossroads group, led by Karl Rove – even Americans for Prosperity, bankrolled by the Koch brothers, conservative billionaires and demons of the left, who have supported many Tea Party candidates.

Not this time though, and the strategy worked. Tillis cruised to victory in the primary over his Tea Party opponent, an obstetrician named Greg Brannon, who said food stamps were equivalent to slavery, and inter-state toll roads are fascism. And Brannon's defeat, some argue, marks the beginning of the end for the tea party.

The movement, legend has it, was born of a primal scream of a rant by a commentator on the CNBC business cable channel in early 2009, at the darkest moment of the Great Recession. Quickly it became the driving force of the party, powering Republicans to a majority in the House of Representatives in the 2010 midterms, in one of the biggest swings in American political history. Many of the 87 new Republican Congressmen were, like Brannon, without political experience and contemptuous of compromise, determined only to change a "Washington" they regarded as the fount of all evil.

In 2012, a dozen of them lost their seats, but Republicans comfortably retained their House majority, although they failed to capture the Senate (in part because of poor Tea Party candidates). If anything, the Tea Partiers were more obstreperous and rebellious than ever, but John Boehner, the Speaker, still rode the tiger – in the belief that harnessing their energy and convictions was the way forward.

But the would-be revolutionaries over-reached. The turning point, in retrospect, was last October's government shut-down, demanded by the zealots as a means of extracting changes in Obamacare. Boehner opposed it but failed to prevent it; and the land's highest ranking Republican was exposed as an emperor with no clothes. The shutdown was a PR disaster too. Americans realised they did need a functioning federal government. Overwhelmingly they blamed the Republicans, who were saved from utter disgrace only by the near-simultaneous botched launch of Obamacare.

At that point the party establishment – big business, big donors and grandees like the Bushes – collectively decided, enough. Bad candidates were a big reason why Republicans had failed to win the Senate in 2010 and 2012; in 2014 they would not make the same mistake again. And the strategy seems to be working.

Tea Party challenges to incumbents were repelled in Texas and are losing steam elsewhere. On Tuesday, Boehner easily won the primary in his Ohio district. According to a new Gallup poll, support for the movement among Republicans and Republican-leaning independents has dropped to 40 per cent, from over 60 per cent in November 2010.

But the end of the Tea Party? No way. For one thing, few of their number are under challenge in primaries. More important, the movement has in many respects achieved its goal, by shifting the Republican party to the right. In North Carolina, Tillis may be a seasoned politico, who knows his way around elections. But he's conservative enough for almost any taste. What's changing is not so much the ideology of candidates, but their presentability. The Rinos may seem to be winning. In reality, they've already lost.