MPs and peers who backed the assisted dying bill now believe it is “near impossible” for it to pass the House of Lords in time because of procedural obstacles used by opponents.

Supporters of the bill, including its sponsor, Kim Leadbeater, have been in intense discussions with the government to find ways to move it to a vote in the Lords. With progress so slow, experts and MPs believe it is unlikely the legislation will even be put to a vote before the end of the session in May, after which it will automatically fall.

MPs told the Guardian they were in “blind fury” about the apparent inevitability of the billing falling in the Lords despite passing the Commons. “It is our system at its absolute most dysfunctional,” one MP said.

Several MPs named the former Conservative ministers Michael Gove, Thérèse Coffey, David Frost and Mark Harper as peers who were determined to stop the bill. Peers deny they are deliberately filibustering and say the bill is so flawed it merits all the scrutiny it is receiving.

One source said MPs should have expected the bill to fall in the House of Lords, which was “routine” for private members’ bills.

The bill would legalise assisted dying in England and Wales for those with a terminal diagnosis and with less than six months to live. Dr Simon Opher, one of the Labour MPs on the bill committee who undertook its original scrutiny before the Commons vote, said: “This is an absolute disgrace. Many MPs who voted against are also outraged.

“I believe this is a real threat to our democracy and in the end will hasten the abolition of this unelected second chamber. It shows our system doesn’t work and is fundamentally undemocratic.”

A minister said: “They are making a mockery of our parliamentary system and bringing parliament into disrepute.”

Another MP said there was now a clear case for extensive Lords reform. “Parliament expressed a clear democratic will. The public are hugely in support. We reformed the Lords a century ago when they frustrated the will of the people [the budget of 1909 was rejected in the Lords, after which the chamber lost its ability to veto legislation]. We can do it again. The Lords can stand for election.”

Leadbeater said on Wednesday she was finding it hard to tell members of the public the bill was not yet certain. “Every day a member of the public comes up to me to say thank you for changing the law, and I have to tell them that we still have to pass the Lords,” she said.

Several of the bill’s parliamentary backers told the Guardian they did not believe there was any amount of time that the government could grant that would stop opponents using procedure to eat up more time until the end of the parliamentary session.

“They show no interest in making progress,” one peer said. “They give near identical speeches, make no unique points, talk for the sake of it, they send people to speak in the debates before our bill starts to run down the clock as much as possible.”

Another said: “It shows the true power of the House of Lords which is rarely used. You can have a handful of people who can use the power to call votes, decouple amendments and just throw sand in the gears and the Speaker doesn’t have the power to stop it or to control the business.”

A source close to Leadbeater said she was aware of the frustrations and had been meeting MPs of all parties to try to convince them it was not hopeless and to hold their nerve.

Opponents of the bill reject the accusation they are using “dirty tricks” to stop its passage and say the sheer number of amendments and time for debate is because it is in an unacceptable state to become law. One senior opponent said it was entirely normal for private members’ bills to be blocked by the Lords.

“From the moment it went to the Lords supporters of the bill have been disingenuous about its chances of passing and the normal processes in the Lords,” the source said. “They’ve continually set false expectations, which seem designed to fail, and do a disservice to parliament and the public.”

The Labour MP Florence Eshalomi, who opposed the bill, said it was right that peers should take their time to scrutinise it. “Not a single royal college, professional body or cabinet minister will attest to the safety of this bill,” she said. “Scrutiny should never be conflated with obstruction and it would be reckless for Lords to ignore the concerns of such a wide range of experts.”

Multiple extra days of debate have already been added in the House of Lords. Last week Charles Falconer, the Labour peer leading the bill through the upper house, was granted further time to allow the Lords to sit later to hear more debate.

More than 1,000 amendments have been tabled to the bill. Last Friday, just four groups of amendments out of the 72 remaining groups were debated. Of those, an hour was spent on the language used in the bill, changing the wording “assistance to end their own life” to “medical help to commit suicide by provision of lethal drugs”, which was proposed by Lord Frost.