Campaigners claim the vote will mean thousands of ill and disabled people will see their benefits cut.
Several residents in Louth and Horncastle have attacked the Government decision.
However,Ms Atkins said there seemed to be a lot of confusion surrounding what the cuts will actually mean.
She said: “I know a lot of people from my constituency are concerned following the ESA cuts. I have read into this issue with great care and there seems to be a lot of misunderstanding going around in regard to what these cuts mean.
“People who are currently in receipt of the ESA allowance will continue to receive this support beyond April 2017.
“The cuts apply to new claimant applications. “I will be keeping a very careful eye on the implementation of what’s to come and if anyone feels issues need addressing, then please let me know. We are trying to change the attitude in the work place and make sure those that can work do get the support. Any money that is saved will be ploughed back to provide this support to get people into work.”
A number of readers have hit out following the decision.
One said: “There are so many people out there who are sick/disabled through no fault of their own and deserve to be supported and what they do get in benefits really doesn’t furnish them with a lavish lifestyle.”
Another resident said: “The Government need to pick on the higher up before hitting the down and outs.”