I'm not sure it would remain a partisan issue if a national ID were used, assuming that there were also good mechanisms in place to make sure everyone can easily get their ID card for free.
The reasons attempts to require voter ID at polling places is currently a partisan issue include:
1. The level of voter fraud is very low, and what little there is almost always would not be prevented by voter ID at the polling place. It usually takes place by absentee ballots, or is based on registering people to vote who should not be eligible (which can be addressed someone by ID requirement--but at registration, not at the polls).
2. When deciding what forms of ID are acceptable, there has been a remarkable correlation between whether a given form is allowed, and whether or not a significantly larger fraction of white voters have that form of ID than do black or Hispanic voters.
3. The same people that pass these voter ID laws have also, in many states, cut the budgets of the state agencies that issue IDs, generally be closing offices that can issue IDs and reducing the hours of those that remain. The closures have tended to be of offices that serve largely black or Hispanic populations, and the cutbacks in hours of the remaining offices have tended to eliminate weekend and evening service. I've read several stories about people who to get an ID had to take a two hour bus ride to reach one of the remaining offices, and had to take a day off work to do it, which was quite a hardship for them.
In short, the current push for voter ID has almost nothing to do with insuring the integrity of the election process. It's about trying to make it harder for to vote for groups of voters that have historically voted against the party that is pushing for voter ID laws.
If we had a national ID, issued by the Federal government rather than state governments, with a strong commitment to make sure everyone who was eligible received their card, and a Federal law that said any state voter ID check must accept the national ID card, it could probably be done in a way that avoids #2 and #3.