Labor could be forced to bring on immediate funding for new in-home aged care services as the Coalition, Greens and crossbench MPs team up in the Senate, angry the government has refused to address growing shortages before a new system begins in November.

Delays in aged care services dominated federal parliament on Monday, with the Coalition using all of its questions in the House of Representatives and the Senate to press Labor over community frustration.

A Senate inquiry heard last week more than 121,000 people were waiting for assessments for in-home support, with the official waitlist for approved recipients already at more than 87,000 people.

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The approximately 2,700 packages being released each week are existing places being reallocated from recipients who have died or no longer require in-home care.

Public servants told the inquiry they were ready to proceed with allocation of new in-home places, with only the government’s decision to delay rollout of its new Support at Home program until 1 November holding up progress.

Support at Home is replacing existing home care packages. Originally slated for introduction on 1 July, Labor expects the new scheme to reduce maximum wait times to 90 days by 2027.

Independent senator David Pocock, the Greens’ Penny Allman-Payne and the opposition aged care spokesperson, Anne Ruston, have negotiated a deal to support amendments to government legislation designed to force immediate allocation of new home care places and front-load the new home care system to meet demand.

The vote is expected to deliver Labor a defeat in the Senate as soon as Tuesday.

Allman-Payne wrote to the minister for health and ageing, Mark Butler, on Monday night, saying families were being told by doctors to admit their parents or grandparents to hospital because they could not access aged care services.

“It is clear that the government’s refusal to release more home care packages is rippling across our healthcare system, in particular the availability of hospital beds,” she said.

“The Greens are gravely concerned about the health of the aged care system and what this means for our ageing population.

“A shortage of beds, a rationed home care system, and a funding model that rewards wealth and preferences the profits of providers over people’s quality of life will leave pensioners and older renters without the care they need. They deserve better than that.”

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But the aged care minister, Sam Rae, told parliament that since 2020 demand for the home care program had grown from 155,000 people to more than 300,000 people, with budget growth of about 800% in a decade.

“This short delay to commencing the new Aged Care Act is about ensuring the programs like Support at Home are fully ready for older Australians and their families,” he said.

Last week Guardian Australia reported warnings from Kathy Eagar, a former adviser to the aged care royal commission, that the new program is so poorly designed it will fuel demand in already overstretched public hospitals and residential facilities.

Eagar, an expert in health and aged care at the University of New South Wales, told a Senate committee the Support at Home program is “fundamentally flawed” and the government’s forecast that it will reduce demand for residential care is not credible.

The prime minister, Anthony Albanese, said the May federal election had contributed to the delay in rolling out the new system.

“We got feedback from the sector that they wanted to make sure it was got right, to make sure that we got the detail right,” he told ABC TV.

“But this isn’t a pause. People are still getting priority support and still being looked after.”

Demand for aged care is expected to surge in Australia, with the country on track for a doubling of people over 65 and a tripling of those aged over 85 within 40 years.