Legalize the people who are already here, with a permanent guest worker program, but make them ineligible for citizenship.
This gives the immigrants something substantial: they get the right to work, and their children will be citizens. But it doesn't generate 11 million new Democratic voters in the next ten years. If you're worried about things like public assistance, phase in a right to various entitlements over a period of years: so many for Social Security, so many for food stamps.
But while it helps immigrants by normalizing their status, it also has something for people who want tighter border enforcement: a penalty. The price of coming here illegally is that you don't get to be a citizen. You can live here and work here, and retire here and collect the social security benefits you've accrued. But you can't vote, and you can't have an American passport, because you broke the laws about who can live here.