Ted Cruz is looking cocky. Rocking Ray-Bans and an “I Voted” sticker on his lapel — it’s the first day of early voting in Texas — he is easing his way across the parking lot of his local polling place, toward TV cameras set up beside his campaign bus. Backed by sign-waving fans, he starts his brief remarks, only to be interrupted by an angry man shouting from a few yards away: “You’re a traitor to democracy!”

Some pro-Cruz women yell back, and the heckler wanders off through the parked cars. Mr. Cruz seems not to even notice, plowing ahead with his call to “Keep Texas Texas” — his campaign motto — and talking up jobs, freedom and security. (That last category consists largely of horrifying stories about violent crimes perpetrated by “Venezuelan gang members.”) He takes shots at his Democratic opponent, Representative Colin Allred, whom he calls a formidable candidate “if he were running for City Council in San Francisco.” (Mr. Cruz uses this line at multiple stops. It’s a real crowd pleaser.) And when asked if he’s concerned about the influx of new voters to Texas in recent years and the state’s shifting demographics, he fires back with absolute confidence:

“We’re going to win.”

With his buoyant delivery and smug smile, Mr. Cruz wants to remind you of something: He is never happier than seeing a liberal fantasy and crushing it. The Democratic dream of turning Texas blue is approaching middle age with nothing to show for it, but this particular hope never dies — and the goal of ousting Mr. Cruz, a bête noire of Democrats if ever there were one, will endure as long as he’s in office. As in his last race in 2018, he is Democrats’ top Senate target this year, with recent polling showing him just a few measly points ahead of Mr. Allred, generally within the margin of error. And once again he is being dramatically out-raised by the Democrats, a disparity made worse by the millions of dollars that national Democratic groups are pouring into the contest. It’s not just that the Democrats see unseating Mr. Cruz as their best shot at holding onto their Senate majority. They also see him as the most promising opportunity to break the Republican Party’s multidecade lock on statewide offices here — giving them that first crucial step toward their dream of turning Texas, if not blue, then at least purple.

But don’t look for Mr. Cruz to crumble. This is basically how he rolls. The senator was a divisive, bomb-throwing, lib-owning loudmouth years before Donald Trump entered the political arena, basking in his critics’ hate as if it was winter sunshine. He is known for annoying his own teammates with bone-headed moves. (Remember “Green Eggs and Ham”?) Yet he somehow manages to be disruptive and bombastic enough to impress Texas Republicans without alienating at least a portion of the state’s independent voters. And his in-your-face partisanship may help him walk an ideological line that might trip up other, subtler Republicans.

In a party where Mr. Trump has dragged down candidates and upended elections for years, with so many Republicans redefining themselves in his image, Mr. Cruz has stood out as a pretty indestructible character for someone so disliked. Or if not indestructible, he persists, and persistence can go a long way in Texas politics. It helps that voters here like their politicians on the scrappy side with a dash of sass. (Pace, Ann Richards and Lyndon Johnson.) It also helps that Mr. Cruz knows how to modulate his extreme partisan jerkiness when useful. Even many voters who find him personally insufferable — and they are legion — wind up pulling the lever for him.

Admittedly, this isn’t the prettiest or easiest way to stay in office. In 2018, he came within less than three points of losing re-election to Beto O’Rourke, who was then the Texas Democrats’ star of the moment. And who knows? This election, a less flamboyantly grating Republican candidate might very well be on a glide path to victory rather than locked in a dogfight. Still, Mr. Cruz’s unique brand has served him well enough — and attracted a curious coalition of voters who will probably be enough to win him a third term on Nov. 5.