Lectures about fiscal responsibility from the occupants of a plush suite on the 20th floor of one of the fanciest hotels in Las Vegas stick in the craw like a slice of cantaloupe swallowed sideways. Appropriately, the Tea Party Express's open bar, trays of fruit and skyline view at the Aria hotel on election night smacked more of a corporate event than a political, let alone a populist, one.

At one stage I turned to a man standing next to me and asked if he was a Tea Party supporter. "No," he said. "I was hoping you were." He was a state department official who had brought some foreign journalists in the hope of meeting some real Tea Party supporters to interview. But they couldn't find any. There is a reason for that.

The "Tea Party" does not exist. It has no members, leaders, office bearers, headquarters, policies, participatory structures, budget or representatives. The Tea Party is shorthand for a broad, shallow sentiment about low taxes and small government shared by loosely affiliated, somewhat like-minded people. That doesn't mean the right isn't resurgent. It is. But the forces driving its political energy are not those that underpinned its recent electoral success.

The Tea Party is not a new phenomenon. It's simply a new name for an old phenomenon – the American hard right. Over the last two years the term has provided a rallying point for a coalition of disparate groups, most of which have been around for many years. Minutemen (anti-immigrant vigilantes), birthers (who deny that Obama was born in the US), Promise Keepers (Conservative Christian men), Oath Keepers (military and police, retired and current, who vow to resist unconstitutional government "by any means necessary"), Fox News watchers, Glenn Beck lovers and Rush Limbaugh listeners who had no unifying identity before.

Having a name helps. It has offered a political identity to a significant number of people who were either not active or might not have understood themselves to be in any way connected. That name has helped reorient the stated priorities of the right away from social issues and towards fiscal ones. But this is no more than the old whine in new bottles.

Most of the characters now closely associated with the Tea Party are not new to rightwing politics. They have just moved from the margins to the mainstream. Sharron Angle, the failed Senate candidate from Nevada, has held state office since 1998. While in the 42-member state assembly she voted no so often on consensual matters that such votes were sometimes referred to as "41-to-Angle". The much-maligned Delaware Tea Party candidate, Christine O'Donnell, stood unopposed in the Republican primary in 2008 before going on to challenge Joe Biden. These people didn't join the Tea Party, the "Tea Party" term attached itself to them.

It is difficult to imagine a candidate earning the Tea Party label who is not against gay marriage or abortion, for the simple reason that no such candidate could exist. White Christian evangelicals still formed one of the most crucial bedrocks of last week's Republican success – comprising 25% of the electorate and giving 79% of their vote to the GOP. That's far more clout than black and Latino votes combined give the Democrats .

At first the term Tea Party helped us understand the insurgent, inchoate force that took to the streets last year; now it may be hindering analysis of its more choreographed march to power. For when people ask what the Tea Party will do, talk about Tea Party demands, or lay down Tea Party threats, they mistake (wilfully or otherwise) the Tea Party for a coherent formation with power of cohesive action. It's not.

Research conducted over several months by the Washington Post to contact every Tea Party group in the country found that many did not exist. Seventy per cent said they had not been involved in a political event in a year – a year in which the Tea Party was credited with transforming the nation's politics.

"When a group lists themselves on our website, that's a group," Mark Meckler, a founding member of the Tea Party Patriots, told the Post. "That group could be one person, it could be 10 people, it could come in and out of existence – we don't know."

This is less of a criticism than a description. Movement-building is hard, messy work that, if it is to be truly at grassroots level, produces uneven results. In that sense it's no different from, say, the anti-war movement, and would have been about as successful were not it for two key factors.

The first is that the Tea Party has its own "news" channel – Fox – devoted to its growth. It promotes Tea Party demonstrations as though they are events of national celebration and showcases those who pose as its leaders as though they are national celebrities. Second, it has money. A lot of it. When it comes to elections it has the backing of huge amounts of money from private corporations and individuals who are behind institutions – like the Tea Party Express, Freedomworks, Americans for Prosperity and Tea Party Patriots – which are run by people with a proven track record of rightwing Republican activism.

The relationship between these organisations and the base of people who call themselves Tea Party supporters is episodic and erratic. They show up in different places where they sense an opportunity for a breakthrough, throw money at it, attract media attention for it, and then see what sticks. Sometimes it works, sometimes it backfires – mostly it makes barely any difference. They have no organic, let alone democratic, relationship with the grassroots that they claim, in some way, to represent. Sarah Palin, for example, endorsed 64 candidates this season. Half of them won last Tuesday; 10 lost in the primaries, 19 lost in the general elections, and three races are still too close to call. Her support is important, but hardly decisive.

It would be too easy to deduce from this that the Tea Party is simply a creation of big business and the rightwing media. Neither, alone, can explain the 50 or so conservative old men who have met at the Nugget Casino in Pahrump, a hard-scrabble town in rural Nevada, every Friday for the last five years, or most of the other groups I have seen around the country. It would also be too naive to suggest that such groups would boast anything other than a marginal presence without big money and media to amplify their voices.

What we witnessed on Tuesday was not a realignment of American politics but the first real test of the reconfiguration of the balance of forces in the American right. Exit polls show an electorate even more polarised than two years ago, where registered independents swung to Republicans but self-described moderates continued to back the Democrats. Sixty per cent of the seats that the Democrats lost were in districts where John McCain beat Obama in 2008.

Last December I interviewed Rand Paul, after he addressed about 12 people in a small town in Leitchfield, Kentucky, and asked what the Tea Party meant to him. "I call it the national open mic movement," he joked. "It's kind of good in a way. Some people were tired of not being able to speak their piece. But I don't think it has a cohesion yet. It's yet to be seen whether it can transform itself."

Back then Paul was a rank outsider; now he is a senator-elect. The Tea Party still has no cohesion, but it has been transformed. Not from the inside or below, but from the outside and above. Its name reflects a popular mood, its actions reflect an elite capability.