Pro and anti-abortion MPs are preparing for the first full Parliament debate for 17 years on the 24 week limit.
An attempt is expected to be made this week to amend the draft Human Tissue and Embryos Bill, calling for the upper time limit to be reduced.
Ann Widdecombe MP said the public wanted a debate, as babies born at 24 weeks had a chance of survival.
But Evan Harris said MPs should debate whether the law needs modernising and extending to Northern Ireland.
Both MPs, on opposing sides of the debate, agreed it was a "disgrace" that Parliament had not held a full debate on abortion for so long.
Three attempts
Commons authorities have indicated that abortion falls within the scope of the Human Tissues and Embryos draft bill, being examined by a joint committee on Tuesday.
Three recent 10-Minute Rule bills have called for changes to abortion law, calling for a compulsory "cooling off" period for women, to end confidential abortion for the under-16s and to reduce the upper time limit to 21 weeks.
"People want this to be debated and resolved, so yes, we will go for it"
All have been substantially defeated and Miss Widdecombe, a Conservative MP, conceded that it appeared that the Parliamentary numbers were not in the anti-abortion movement's favour.
But she told the BBC that while polls indicated most people backed the right to abortion, there was a "general growing unease" about the 24-week limit.
She said: "People want this to be debated and resolved, so yes, we will go for it."
'Deeply wrong'
She added: "What does it say for our moral compass that you can have two children of exactly the stage in gestation, one is in a cot with all the resources of medical science being poured in to look after it - the other is being taken from the womb?
"The only difference between the two is one is seen, one is not seen and there's something deeply wrong with that."
"There is very little evidence that babies born before 24 weeks gestation are viable"
Dr Harris, a Lib Dem MP, said he also expected the time limit to be debated, but he wanted to see "more progressive" abortion measures discussed as well.
Current restrictions forcing a woman to see two doctors first was "not the modern approach to respecting the autonomy of patients," he said.
He wants to see a debate on whether to change the restriction that only doctors can carry out abortions, not other "appropriately trained healthcare professionals", and whether the law should be extended to Northern Ireland.
He added that there was no strong case on "ethical, practical or clinical grounds for reducing the upper time limit".
"There is very little evidence that babies born before 24 weeks gestation are viable in the sense of having a reasonable chance of a reasonable quality of life," he said.
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