When Arizona senator Kyrsten Sinema voted against including a $15 per hour minimum wage in President Joe Biden’s coronavirus relief package earlier this year, she did it with a dramatic flourish: a thumbs down.

The gesture recalled the late John McCain, another Arizona senator who frequently broke with his party and famously gave a thumbs down to fellow Republicans’ efforts to repeal the Affordable Care Act, Barack Obama’s signature health law.

But Sinema also outraged progressives, who singled her out as one of eight Senate Democrats to oppose the wage increase. Sinema’s spokeswoman argued that the media’s focus on her “body language, clothing, or physical demeanour” was sexist.

Three months later, Sinema is once again at the centre of political debate, spearheading bipartisan infrastructure talks with the White House and attracting criticism from inside her own party over her support for the filibuster, an arcane Senate rule that means most bills need the support of 60 senators — or at least 10 Republicans in the current Congress — to become law. Calls to scrap the filibuster grew louder this week after a sweeping voting reform bill died without a single Republican vote.

The emergence of the first-term senator as a congressional power broker highlights the daunting maths confronting Biden as he pushes ambitious plans for infrastructure, clean energy and the social safety net. In a Senate split 50-50 between Democrats and Republicans, centrists such as Sinema and West Virginia’s Joe Manchin wield outsized sway.

Sinema, who will soon turn 45, has made no secret of her desire to inherit McCain’s reputation as a “maverick”. She doubled down on the filibuster with a column in The Washington Post on Tuesday, shortly after the progressive group Just Democracy spent $1.4m to run adverts accusing her of “failing” Arizona voters. Sinema argued that bipartisan co-operation is the only path to “durable, lasting” results.

Biden hosted Sinema for a rare one-on-one meeting at the White House on Monday. A group of senators gathered in her office with administration officials on Tuesday in the hope of hashing out an infrastructure deal that could garner a critical mass of bipartisan support. Jen Psaki, press secretary, said late on Wednesday that a “potential agreement” was within reach, and the senators would visit the White House on Thursday for further talks.

Neil Bradley, chief policy officer at the US Chamber of Commerce, which has given Sinema several awards for her bipartisanship and support of business-friendly policies, said it was a natural fit for the senator.

“The fact that she has trust and credibility with not just Democrats but also Republicans . . . it is like a muscle. You have to build and practice these relationships, and you have to build trust,” Bradley said. “She has spent years doing that, all for the ability to be a key lawmaker in a critical moment like on infrastructure.”

With a colourful wardrobe, statement eyeglasses and neon wigs — which she wore in the pandemic when she could not have her hair dyed platinum blonde in the salon — Sinema often stands out in a sea of dark suits in Washington. But her CV is equally distinctive.

Born in Tucson, Arizona, Sinema grew up poor in Florida’s Panhandle region. She graduated at the top of her high school class aged 16 before attending Brigham Young University, a Mormon-affiliated college in Utah. She later returned to Arizona and earned a masters degree in social work and a law degree.

She left the Mormon church and later came out as bisexual. She is one of two openly LGBT senators and the only member of Congress who identifies as “religiously unaffiliated”, according to the Pew Research Center.

Two decades ago, Sinema was a member of the Arizona Green party, an antiwar activist and self-described “Prada socialist”. But after finishing last in a field of five candidates for the state legislature, she joined the Democrats and won election two years later in 2004.

She steadily built a reputation as a moderate, first at the Arizona statehouse and later in the US House of Representatives.

Her move to the centre has made Sinema open to accusations of hypocrisy. But critics and allies alike say the senator has been savvy in her pursuit of power in Arizona, a border state in the desert south-west where roughly a third of registered voters are unaffiliated with either main party.

Republicans dominated statewide elections for decades with free-market economics and tough immigration policies. But Democrats have made inroads, helped in part by influxes of immigrants from Latin America and people from California and other states.

In 2018 Sinema became the first Arizona Democrat to be elected to the Senate in 30 years. “She has made some very shrewd political calculations that have taken her all the way to the US Senate,” said Chris Love, chair of Planned Parenthood Advocates of Arizona, the group’s political arm.

She won with the support of centrist Democrats, independents and Republicans disillusioned with Donald Trump. Last month 45 per cent of Arizona voters held a favourable view of Sinema, a rebound from two months earlier, when her approval rating slipped to 39 per cent following the minimum-wage vote, according to a poll by OH Predictive Insights, a non-partisan research group in Phoenix.

“Hard right or hard left does not do it in general elections here,” said Mike Noble of OH Predictive Insights. “What does win statewide is centre, centre-right or centre-left.”

Noble said the latest results demonstrated Sinema — who is not up for re-election until 2024 — was unlikely to be penalised by voters for going against the grain.

But that does little to reassure progressives.

“There is latitude . . . people understand it is a moderate state, she needs to have these moderate positions,” said Catherine Alonzo, chief executive at Javelina, a Phoenix-based consultant to companies and political campaigns. “I just think that for a lot of people this is just a bridge too far.”