A 55-year-old Baghdad University engineering professor, Muayyad al-Samarai said on Wednesday that Iraq could not be stable if the US-led forces left.
"Iraqi forces don't have the required level of training to protect the country," he said.
But real estate agent Ali al-Jibouri, 45, disagreed, saying only Iraqi politicians were benefiting from the foreign presence.
"Everything was plotted by the Iraqi politicians who came from abroad to prolong the time of the occupation because it will serve their personal interests," he said.
Bush's speech on Tuesday night at a US Army base in North Carolina came on the one-year anniversary of the handover of partial sovereignty, but many ordinary Iraqis still believe the presence of about 135,000 US troops prevents local officials from fully controlling internal affairs.
"The transfer of authority was a great dream but nothing took place," said Samah Abd al-Muhsin, a 24-year-old housewife living in al-Amin al-Thaniyah in eastern Baghdad.
"Bush does not want to pull out the American forces although we can defend our country. There are so many problems because of the presence of foreign troops."
Other Iraqis went further, insisting a US timetable for withdraw would reduce pressure on civilians who were weary of daily bloodshed.
"We haven't felt any change since the transfer of authority last year and the reason behind that is the lack of a withdrawal timetable"
Saeed Yasin Moussa,
Oil Ministry employee
"We haven't felt any change since the transfer of authority last year and the reason behind that is the lack of a withdrawal timetable," said Saeed Yasin Moussa, 52, an employee at the Oil Ministry who lives in eastern Baghdad's Baladiyat neighbourhood.
"The timetable can lessen the psychological pressure on the Iraqi people."
Bush speech indifference
And a senior official of what is believed to be the country's largest Shia political group said Bush's speech - in which he did not give a timetable for withdrawal - probably did not have much resonance with ordinary Iraqis.
Ridha Jawad Taqi of the Supreme Council of Islamic Revolution in Iraq said that "as far as Iraqis are concerned, there was nothing important in the speech".
"But I heard it was important to the Americans... It is necessary not to set up a timetable for the withdrawal of US troops. Their presence is linked to the security situation here."
A Sunni Arab politician disagreed, saying members of his community had been marginalised by the US-dominated political process and by Iraqi security forces.
"The country is now run by the Shia and the Kurdish alliances," said Ayad al-Samarrai, a senior official of the Iraqi Islamic Party, a major Sunni party.
"This reflects badly on the political process ... we think that the American way of dealing with the situation here either reflects a failure to understand the nature of the place or shows that they're not working as seriously as they should be."