It comes as the public service agency has proposed cutting 447 jobs.
The legislation is coming up for review later this year.
It claims it is still recruiting to fill shortages.
There is concern more people will be arriving on the doorsteps of budgeting services.
MP Cameron Luxton submitted the bill, saying current restrictions are "dumb".
"The law is the law and if that needs to change that's really not a matter for me."
The Government released nine targets for various public services.
"Let’s be very clear the Suicide Prevention Office will remain open."
People are worried about their financial futures as the Government makes sweeping cuts.