Ireland was forced to review its abortion law in cases where the mother's life is at risk following the death of Indian dentist Savita Halappanavar in a Galway hospital last October after she was denied an abortion.
The government-drafted Protection of Life During Pregnancy Bill has strongly divided the Catholic country.
An inquest into 31-year-old Savita's death earlier this year was told that a timely abortion may have saved her life.
The laws will be supported by the vast majority of the country's politicians, but they are likely to see the fall of a junior minister who has shown signs of joining a small backbench revolt.
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Despite minister for European affairs Lucinda Creighton's widely anticipated rebellion, the laws are likely to pass with a majority.
Hate mail and death threats to politicians, and intimidation of campaigners have raged throughout the divisive abortion debate.
Outside the parliament hundreds of anti-abortion protesters, who had spent the night reciting prayers with rosary beads, vowed to spend a second night kneeling on the spot in hopes of inspiring lawmakers to rebel against Kenny.
"Keep abortion illegal - babies can LIVE without it," their placards read.
While Ireland officially outlaws abortion in all circumstances, its laws on the matter have been muddled since 1992, when the Supreme Court ruled that abortion should be legal in cases where doctors deem a woman's life at risk from continued pregnancy - including, most controversially, from her own threats to commit suicide if denied one.
But Ireland faced renewed pressure to pass legislation on medical-emergency abortions after the European Court of Human Rights ruled in 2011 that Ireland's inaction meant that pregnant women in medical crises faced potentially dangerous delays in receiving terminations in neighbouring England, where abortion was legalised in 1967.