Bolton Council has proposed to bring in the restrictions in streets around Daisy Hill and The Hoskers.
The new speed limit would apply to the roads south of the railway between Leigh Road and Wearish Lane and Hydrangea Close to the east of Leigh Road.
But members of Westhoughton Town Council, which discussed the plans at a meeting on Monday, believed there were more roads that needed to be included.
Cllr Lynda Winrow-Baker said: "I can't believe they have missed out Hartford Road. It is so dangerous and there have been so many accidents and they still ignore it.
"I really think they should include it."
The plan is part of the borough-wide rollout of 20mph limits to tackle speeding and potential injury in residential streets.
Cllr David Wilkinson agreed that some motorists needed educating and said he saw a car almost lose control in Westhoughton recently.
He said: "I was coming home on Friday and there was a lad coming up Church Street so fast he nearly lost control and went across towards the chemist.
"If anyone had been coming over the zebra crossing it could have been really serious.
"I think there are roads missed out but I do agree that we need to change drivers' attitudes. I walk around Westhoughton all the time and I have seen some absolute idiots.
"Hopefully this rollout will have an impact. I think there are parts that should have been looked at properly.
"I would like to look at including other roads in the area."
Cllr David Chadwick said: "You can't legislate for idiots. We have got to change the attitude of people because there are far too many children and elderly residents getting injured.
"We have got to change these drivers' attitudes."
The town council voted to ask Bolton Council whether other roads, including Hartford Road and Hindley Road, could be looked at.
A Bolton Council spokesman said: “In 2015 we made a commitment to making all appropriate residential roads in Bolton 20mph.
"Roads which are not included for speed limit reductions may not be suitable due to their role and the nature they are used in by road users travelling about the borough.
“Work on the first phase of the 20mph programme has finished ahead of schedule, benefitting two thirds of residential roads – around 50,000 households - in the borough.
“Work is now underway on the remaining residential streets suitable for reduced speeds.
"This will benefit a further 1,261 streets and roads in: Astley Bridge; Bradshaw; Breightmet; Bromley Cross; Harper Green; Heaton; Horwich; Hulton; Lostock; Smithills, and Westhoughton. These wards do already have some 20mph speed limit areas.”
Comment on the proposals can be submitted until Tuesday, May 23.
For more information, go to bolton.gov.uk