"Maybe we will follow in the steps of our Jewish brothers," he says.
The priest's reference to Iraq's Jewish population – once a thriving community numbering in the tens of thousands but now practically non-existent – neatly sums up the possible fate of Iraq's Christians.
The 2003 US-led invasion of Iraq ended Saddam Hussein's disastrous rule, but also turned the country into a battleground between insurgents and foreign troops, unleashing a wave of bombings and killings by militants in which Christians were not only caught in the crossfire, but targeted themselves.
The bloodiest single attack on the community happened on October 31, 2010, when Islamist militants killed 44 worshippers and two priests in Baghdad's Our Lady of Salvation church.
Cacha compiled a book documenting the attack and its aftermath.
Some pictures in the book were taken soon after the assault, when bodies including those of young children still lay in pools of blood on the church's dusty, rubble-strewn floor. Others show later scenes including memorials for the dead, and the wounded in hospital.
The attack "was a catastrophe for the Christians, and it broke the back of our presence in this country," says Cacha. "It is the catastrophe that led to emptying the country of Christians."
The UN refugee agency said thousands fled after the October 31 attack, which was claimed by al-Qaeda.
Estimates of the number of Christians living in Iraq before 2003 vary from more than one million to around 1.5 million. But repeated attacks by Islamist groups pushed many to leave, and now they are estimated at less than 500,000.
Churches remain targets
Between 2003 and May 2012, some 900 Christians were killed, while 200 were kidnapped, tortured and ultimately released for exorbitant ransoms, according to the Iraq-based Hammurabi Organization for Human Rights (HOHR).
Around 325,000 Christians have left their homes for other areas of Iraq, according to the organization.
"There were 300 churches in Iraq, and now there are only 57 left. Even those that remain are targets," according to Louis Sako, newly-elected Patriarch of the Chaldean Catholic Church, the largest Christian church in Iraq.
Figures at the local level are similarly bleak.
Cacha said of the 1,300 families that once frequented his church, there are now only 400-500, while a Chaldean priest put the figure for Christian families in the southern port city of Basra at 450, less than half the 1,150 families in 2003.
All that despite being Christians, being among the ethnic and religious minorities represented in the Iraqi parliament – Christians have one cabinet minister, five MPs, and hold provincial council seats in Baghdad, Nineveh in the north and Basra in the south.
Apart from those cities, the community is concentrated in the Kirkuk, Dohuk and Arbil.
The vast majority are part of Sako's Chaldean Church, an Eastern Rite Church recognized by Rome which uses Aramaic, the ancient language that Jesus Christ would have spoken.
The situation in the wider Middle East region is also causing concern for Christians and other minorities as Islamists take an increasingly tighter grip on power following the Arab Spring.
"The coming years will be very difficult for Christian groups in the Middle East and the Arab world. There will be challenges for how to secure them and protect their rights, privacy of religion and traditions," said Saad Sirop Hanna of Mar Yusuf Church in central Baghdad.
"I don't know how mature the political leaders and politicians of the Arab Spring are to understand this challenge," he said, also expressing fears that Christians could get caught up in a conflict between Sunni and Shiite Muslims.
The future of Iraq's Christian community ultimately hinges on whether the current lack of security and jobs can be resolved.
"Many Christian youth want to emigrate, and when I ask them why, they say, 'Give us jobs to live and safety to stay,' and that is something I cannot answer," said former migration minister Pascal Wardeh, who now heads the HOHR.
If the violence and instability continues, it risks driving the once-thriving Christian population, like Iraq's Jews, out of the country and into the history books.