We've been saying for a long time that the government should be contributing to EI, in general, as they did prior to the 1990s. It would help a lot if they were contributing for extended benefits during these difficult economic times on an ongoing basis.
It sounds like a good fix, but I know that in Quebec there was a hue and cry about getting the government to fund part of the employers' portions there. The one thing I would caution you about is that there may be some backlash among those who are payroll employees and participating in the program if there are government contributions towards the self-employed from general revenues and not likewise for the payroll employees.