Lytle is a blink-and-you'll-miss-it kind of town, one of hundreds that dot the vast flat ranchlands of southern Texas. A smear of houses by the main highway between San Antonio and Laredo. Population: 2,383. The first streets only got paved here in the years after the second world war. A sewage system took a little longer, not being built until the 1960s. In short, Lytle, Texas, has never been big enough to have much impact on the politics of the Lone Star state. And few Texas politicians have ever paid much attention to it.

Until Debra Medina, that is. When Medina breezed into Lytle's community hall the locals found themselves confronted with a Texan version of Sarah Palin. She wore a sharp scarlet skirt suit, librarian-style glasses and a puffed-up hairdo. More than 60 Lytle residents had gathered to meet her, a hefty turnout on a weekday at 11am for a Republican primary election in the race to be Texas governor. Medina has become a political phenomenon in Texas. Emerging as a genuine star of the rightwing populist Tea Party movement, she delivers a fiery message of slashing taxes and the abolition of almost all forms of federal government, and issues dire warnings that President Obama is taking America down a slippery slope to Soviet-style communism.

It's working. Previously unheard of by the vast majority of Texans, Medina has set the race for governor on fire, upsetting the primary contest between the incumbent, Rick Perry, and Senator Kay Bailey Hutchison.

Those gathered to see Medina in Lytle loved her. Young and old, men and women, Latino and white, listened with rapt attention as she outlined her agenda and asked them to back her in this week's first round of voting. If she can beat Hutchison into second place, she can secure a runoff against Perry. That would raise the possibility – distant but real – of a Tea Party activist capturing the government of the second biggest state in America. The Tea Party movement would have gone from being a bunch of ragtag protesters to heading one of the largest single economies in the world. "If we can change politics as usual in Texas, then we can change politics as usual across America. This is not just about Texas, but about changing the whole country," Medina told the Observer before addressing her supporters in Lytle.

She is not alone in that ambition. Across America other extreme candidates have emerged on the Republican right to challenge familiar party figures with a fiery mix of Tea Party-inspired populism. In Arizona, Senator John McCain is facing a tough re-election fight against a former congressman, JD Hayworth, who has expressed public doubts as to whether Obama was born a legitimate American citizen. In Florida the moderate Republican governor, Charlie Crist, is lagging badly in his own primary election to rightwing challenger Marco Rubio, who has the backing of local Tea Party groups.

On the right of US politics, this is big stuff. Instead of forcing mainstream Republicans to woo them for their votes, the rightwingers are now bidding for power. It is an attempt at revolution that could have huge meaning for America and the world, especially given the disastrous showing of Democrats in recent polls and elections. Medina knows this. After her speech she ended with a plea to her audience. "We can win this race," she said, then held up her hand and squeezed two fingers together. "It is this close."

Later that night, at a firemen's association hall in the much larger city of San Antonio, Medina's face stared down from a huge screen as she delivered a long policy monologue. To her audience she was the very antithesis of establishment power: a heroic revolutionary, out to destroy government and bring power to the people. "She is not a career politician. Everything she is saying will make Texas better than what it is," said Sergeant Shawn Mendoza, 30, a veteran of three tours to Iraq and Afghanistan. A few minutes later the flesh-and-blood version of Medina entered the hall. She got a standing ovation before she had said a word.

She began her stump speech again, still wearing the outfit she had in Lytle. But when it comes to speeches Medina is no Sarah Palin. She has no need to write on her hand to remember her talking points. Instead her speech was a complex walk through her extreme anti-government philosophy, citing sources as varied as the Austrian school of economics, St Augustine and modern French philosophers. She said she wanted to get rid of property taxes and allow Texans to do whatever they wanted with anything they owned, whether that was dig for oil or build an extension. There was, she said, no constitutional basis for a federal Department of Education or an Environmental Protection Agency or the Federal Reserve. Texas should assert its rights almost as a nation-state, controlling over its own National Guard units. The disdain for government was visceral. The American way, she said, was simple. "There are two rights essential to freedom: private property and gun ownership."

Such thoughts find fertile ground in Texas. This state has always had a swaggering, independent streak and a dislike for too many laws. Medina was born on a farm near the small town of Beeville in south Texas. She speaks with a homely Texas accent and worked as a nurse before entering politics at county level in the 1990s. Her bid for governor was largely ignored by the media as she crisscrossed the state for 13 months, visiting small town after small town. Gradually she crept up in the polls and forced her way into the televised debates, where she performed strongly. Campaign money began to pour in. One poll puts her as high as 24%, just behind Hutchison and within reach of catching her and forcing Perry into a runoff.

Medina believes she is not really in third place, citing the fact that the polls only telephone previous Republican primary voters, whereas she is bringing in thousands of new supporters. "I feel fantastic. I think we can win this," she said in Lytle.

Only once has Medina slipped up – in an interview she gave to the conservative radio host Glenn Beck. On his show Medina was asked if she thought the US government might have had a role in the 9/11 terrorist attacks. She replied: "I don't." She then went on to expand disastrously upon that answer. "I don't have all the evidence there… I think some very good questions have been raised in that regard. There are some very good arguments and I think the American people have not seen all the evidence there, so I have not taken a position on that," she said.

Those comments provided ample ammunition for her political rivals. Her march forward in the polls was halted and some of her advances chipped away. The only time Medina appeared unnerved in Lytle or San Antonio was when a woman in the audience mentioned the Beck interview and asked her if she was a "Truther", in reference to the conspiracy theory that the government planted bombs to blow up the World Trade Centre. Medina looked flustered and started to answer before saying suddenly: "No! No!" and moving on to a new question.

But such areas are the home ground of the Tea Party movement. At almost any Tea Party event it is easy to meet Truthers or Birthers or those who believe Obama is a closet Stalinist or a Nazi or a Muslim fundamentalist or indeed all three together, no matter how blindingly contradictory such beliefs are. In San Antonio one member of the audience wore an Oath Keepers T-shirt. Oath Keepers are a group of veterans, soldiers or police officers who fear their own government is about to attack the American people or round up conservatives into concentration camps. The oath they have sworn to keep is to refuse to obey such orders. That sort of thing remains a fundamental problem for the politicians from the Tea Party seeking high office.

Calvin Jillson, a political scientist at Dallas's Southern Methodist University, believes the Tea Party can be understood as the latest in a long line of explosions of political rage in America. They include the Populist party that won elections in several states during the 1890s recession and the millions who voted for Ross Perot's presidential candidacy in the 1980s. "These things happen but they burn out like a prairie fire. We are in the middle of it right now but when the economy picks up it will fade away," Jillson said.

Yet the crowd in Lytle could not see any sign of economic recovery. Their rage did not feel like it would fade away. "I'm so mad, it's like chewing nails," said Lytle businesswoman Priscilla Squires, 60. She saw this week's primary as the start of fundamental change in America, while the experts say Medina's Tea Party will crash against the barricades of the ballot box. They are probably right. Yet Texas has always been a little different. "I don't think a Medina win is likely," said Jillson "But nothing is impossible. This is Texas after all."