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Kiran and Bina Salvi, from Bolton, travelled out three months ago to collect their surrogate twins.
Labour MP Julie Hilling called on the Home Secretary Theresa May to intervene during a House of Commons debate.
The Home Office said it was a complex surrogacy application with a lot of checks required.
The children have been awarded UK citizenship, but processing delays mean the family cannot return home.
Bolton West MP Ms Hilling raised the couple's problem in the House of Commons saying: "They are desperate, running out of money and stuck in a hot hotel room in India."
They travelled to India to collect their twins Jai and Leela, who were both born prematurely to a surrogate mother, but have not been able to return home.
'Helpline stalemate'
"When we ring the Passport Office helpline we get a request for a reference but for overseas applications there is no reference number," said Mr Salvi.
"They are adamant there is a reference number and there isn't. There's a toing and froing with them."
Mr Salvi said the couple faced the same...