Donald Trump’s favorite insult for political opponents inside his own party is “Rino” – Republican in name only. By such logic, Senators Joe Manchin of West Virginia and Kyrsten Sinema of Arizona are the epitome of Dinos, two elected Democrats whose dogged resistance to Joe Biden’s social agenda threatens/threatened to upend his entire presidency.

Their standoff with the party’s progressive wing over the price tag of Biden’s ambitious reform package has become almost more of a hazard to his legacy than anything the Republicans, currently in a narrow minority in both chambers of Congress, can throw at it.

That resistance – and threat – to Biden’s domestic ambitions is now set to continue for the month of October as House speaker, Nancy Pelosi, set a new deadline of 31 October for the House to pass a major infrastructure spending bill after a week of negotiations left massive social and environmental policy overhaul plan in a limbo.

Progressive Democrats in the House have refused to vote on the infrastructure bills leverage in negotiations over a separate bill that contains huge spending on issues increased access to childcare, help with college tuition and major action on climate change.

Analysts, meanwhile, question if the senators’ resistance to programs that Biden ran and won an election on is rooted more in a need for political self-preservation.

Manchin is a moderate Democrat in a state where the governor’s mansion and both legislative chambers are controlled by Republicans; Sinema is seen as vulnerable in Arizona where she captured the Senate seat that previously belonged to the Republican Jeff Flake before he decided not to run again. Both face sticky re-election challenges in 2024.

Meanwhile, New York magazine’s Intelligencer coined a phrase for the oversized power resting in the hands of the two otherwise unremarkable Democratic holdouts: Manchema. “They are, in effect, holding the president’s priorities hostage to their personal whims,” the article’s author, Sarah Jones, wrote.

“That’s not a new story in politics. But their stubbornness in the face of contemporary challenges reveals the bottomless emptiness of their brand of centrist politics.”

Manchin, 74, has been in the US Senate since 2010, and became a controversial figure during the Trump administration by allying himself on several key votes and even toying with an unprecedented cross-party endorsement of the former president for reelection. If Senate Democrats were frustrated with him then, it morphed into impatience when the party seized control of the chamber in 2020 but became reliant on him for every vote so vice-president Kamala Harris could break a 50-50 tie.

Manchin has always insisted he is not against Biden’s desire to enact social reforms, but balks at the $3.5tn cost and has indicated he would be comfortable with $1.5tn. Last month he called for Democrats to “hit the pause button” for more negotiation.

“I could say that I’m against this and that and everything. I’m for an awful lot of the things. I’m for also putting guardrails on,” he told NBC’s Meet the Press.

Sinema made headlines in 2018 not only for becoming Arizona’s first Democrat senator for more than two decades but also as the first openly bisexual member of the chamber. Yet despite being from the same party as Arizona’s other senator Mark Kelly, who ousted the incumbent Republican Martha McSally in last year’s special election to make it the first time in 70 years the state was represented in the Senate by two Democrats, she has taken a much more conservative stance on several issues.

In March, she angered colleagues by giving a thumbs-down gesture on the Senate floor as she voted against raising the federal minimum wage.

Unlike Manchin, Sinema, who rarely gives interviews, has not indicated publicly what parts of the $3.5tn bill she objected to. As an indicator of her importance to the process, she has become a regular visitor to the White House, getting more face time with the president and senior Democratic leadership than any other senator with only three years’ standing.

In Arizona, Democrats have become weary of Sinema. The state’s Democratic party passed a motion pledging a no-confidence vote if she votes against the bill, while some members are plotting a primary challenge.

In Washington, the Hawaii senator Mazie Hirono encapsulated congressional Democrats’ frustration. “I and others are waiting for Kyrsten and Joe to tell us what is it that they like or don’t like, and then we can get it done,” she said.

Manchin, meanwhile, drew the personal ire of the Senate’s most prominent progressive, the former presidential candidate Bernie Sanders, in a recent interview on ABC’s This Week.

“Is it appropriate for one person to destroy two pieces of legislation?” he asked. “It would really be a terrible, terrible shame for the American people if both bills went down.”