It's a hot Saturday afternoon as Beto O'Rourke is up on stage in the town of Harlingen in the southernmost tip of Texas. He is talking about a blind squirrel.

Outside, the sun is searing, while inside the cool, half-darkened hall a few hundred supporters gather, electrified by his presence. Someone calls out "Beto for president" and the crowd cheers.

O'Rourke tells about the sick squirrel - how his 10-year-old daughter has been caring for it and now the animal can see again. Maybe this is a good sign, he says, the audience laughing at the rodent anecdote.

The 46-year-old is one of the people Democrats across the country have placed their sights on as he tries to achieve the impossible - win the Senate seat from incumbent Ted Cruz. 

Texas, the state of 28 million with its prairies and cattle ranches, oil fields and wind power farms, cotton plantations and large cities, is firmly in Republican hands. The last time that one of its Senators was a Democrat goes back 25 years.

But now O'Rourke wants to unseat Cruz, part of the Democrats' overall hopes in the mid-term elections on November 6 of regaining the majority in both houses of Congress. The chances are not bad in the House of Representatives, but to do so in the Senate the Democrats need to defend all their current seats as well as wrest two away from the Republicans. One of those belongs to Cruz.

O'Rourke is the outsider, and surveys show him running behind. But the very fact that he is given some kind of chance, and that the Republicans are having to spend heavily in what should actually be a sure-fire bastion, makes him a sensation. O'Rourke has collected a record 61 million dollars in campaign pledges, to 35 million dollars for Cruz. Now O'Rourke is tirelessly criss-crossing the huge state in his car, fighting for every last vote.

His appearance in Harlingen is his third on this recent Saturday. The crowd is a colourful mixture of mothers with their kids, pensioners, and many Latinos. O'Rourke, a wiry figure and his shirt sleeves rolled up, stands at the edge of the stage. He gesticulates forcefully with one hand and his deep voice sounds determined. Now and then he'll slip into some Spanish.

"This is nuts. There are 24 days left until we decide the election of a lifetime," he calls out to the audience. In his speech he draws comparisons with how the US did not allow a ship with Jewish refugees into the country in 1939 and Donald Trump's zero-tolerance policy towards illegal immigrants. He talks about families being torn apart at the border with Mexico, about the health system and about military veterans who commit suicide for want of proper care.

O'Rourke's campaign rallies are reminiscent of those of Barack Obama and Bernie Sanders. Like them, he thrills his audiences with visions of a different, better America - in bright contrast to the often dark portrayal of things by Trump. But can all this be enough for a victory in a such deeply Republican state? In the 2016 election Trump won 52 per cent of the Texas vote. Still, the race is closer than appeared conceivable a year ago this time.

On a recent Friday afternoon, an African-American pastor is up on the stage of a rustic-looking saloon in the city of Houston and says a prayer for Ted Cruz. The crowd is smaller than those of O'Rourke, but just as colourful - a mixture of old and young, whites, Latinos and blacks. When Cruz strides out onto the stage the people cheer.

"God bless Texas," the 47-year-old calls out before praising the successes of the Republicans led by Trump - the tax reform, dismantling of regulations, appointing conservative judges to the courts. All this was in jeopardy, he warned, if the Democrats gain the majority in Congress.

In an upper balcony one of those cheering Cruz is Elisa Sharp, a 53-year-old yoga instructor who is wearing a "Women For Trump" hat and makes clear her preferences. She is dismissive of O'Rourke: "He wants open borders," she warns. Elisa herself is not US-born, but came to the country as a child of a family from Mexico. Now, she says, she is proud to be a Texan.

Daniela Sanchez, 32, also supports Cruz. "I believe he is doing a good job. I am Venezuelan and I know the other option is not a good option," she says, meaning the Democrats. Trump and many Republicans conjure up the precarious situation in socialist Venezuela in warning against the Democrats - even though they do not advocate socialism for America.

But Cruz has a problem, says political scientist Jay Aiyer. He is not all that popular in Texas.

On the one side, there is still some "residual unpopularity" dating back to the ugly mud-slinging between Cruz and Trump during the 2016 Republican presidential primaries. As a candidate, Cruz called Trump a "pathological liar" and "a serial philanderer," although the two have since patched things up.

"The other side of it is that Ted Cruz has not been successful in appealing to independents or moderate voters," Aiyer says.

But now Trump needs Cruz to keep his Senate seat and so the president came to Houston recently to stump for him. Two years ago he had called Cruz "lying Ted" but now, all smiles and giving him a hug, Trump calls him "beautiful Ted" and says that nobody in the Senate had helped him more than Cruz had. Cruz says he feels honoured that Trump is campaigning with him.

O'Rourke, meanwhile, is back on the road. He's been campaigning for the past 20 months and the next stop is a rally in the city of San Marcos. Still two weeks to go until the election.