Here's something neither party is suggesting:
Give free IDs to all people eligible to vote. An ID in this case will be a state ID. So you can buy tobacco, alcohol, and hopefully in the future, marijuana, with it. Already have a license or state ID? That works.
Require a voter ID after X amount of time. Let's say 12 years.
Run a national advertising campaign telling people they need an ID to vote.
Use registered voter info and tax fillings to let people know about this and where they can get their free ID.
Get a free ID when you register to vote.
For people who register to vote online, they probably already have an ID. If they don't, let them know they'll need to swing by the DMV to get a free one. Make it so they can fill out all information on the internet except the photo and signature.
Better yet, if an ID is required, why even require voter registration? If you have an ID, you can vote. These kind of IDs are easy to authenticate via swiping it to see if it's in the database.
Write into the law that funding can't be messed with no matter what party is in office unless it's to appropriate even more money to the cause.
If a person who doesn't have an ID, and by some chance hasn't heard of the law, tries to vote in an election. Let them vote, and require the next time they get a free voter ID. You could limit this to people who registered before the law was originally passed if you wanted to.
The organization to administer this is bipartisan with people who have shown they care about making sure everyone gets to vote provided they have an ID.
Optional: Change election date to a better day and or make it a national holiday.
Reminder that requiring an ID doesn't go into effect for X amount of time. Like 12 years. More if required.
This would require compromise from both sides, though. So I doubt it will ever happen.