Ideas to fight for better ratios?

My unit is desiring better ratios(1:3 couplets preferably). Our manager says she has tried but the budgeting people won't go for it. We aren't union. What are some things we can do to fight for better ratios? I'm not sure what management has don't thus far but it's not working and things need to get better!
You could always argue the better staffing = less errors = less money spent due to lawsuits/less risk/liability for the hospital.It's been shown that better staffing actually saves money despite the initial cost of the extra salaries.