In 2006 there was a ballot initiative in California called "Proposition 77". California has liberal laws on putting initiatives out for a vote so they are often a leader in new ideas. The voters use this method to get around the legislature when they do not feel that the legislature is responding to their needs.
Proposition 77 called for congressional (house) districts to be drawn in a bi-partisan manner. These districts would be compact and not designed to favor one party over another. Iowa uses this method (with retired judges selecting the districts) and as a result their house races are all competitive. Nationwide, most house races are not competitive because the districts are drawn to ensure that one party (Democrat or Republican) wins the election.
Proposition 77 was defeated at the polls. The Democrats control the redistricting methods in California and as a result Democratic house members far outnumber their Republican counterparts, even though the statewide balance is far less lopsided. The opposite issue occurs in Texas, for example, where the state has been re-districted to favor Republicans.
These sorts of districts are terrible for democracy because it encourages extremists in both parties. While the majority of Americans are "in the middle", these districts encourage the farthest left people to run and the farthest right people to run. The results are pre-ordained; whomever wins the party primary, wins the election. If you know that you have a competitive election, you appeal to the "middle", but since the primary is the de-facto election, you only need to compete for your respective "fringe".
Now Arnold is trying to horse-trade with the legislature; the legislature wants to eliminate term-limits and he wants to get the redistricting in return. Arnold actually runs from the middle, more or less, and this sort of redistricting would bring forth a much more reasonable legislature, instead of the people on the furthest left and right. This article describes the process under way (which may or may not occur).
If it does occur, you can bet that almost all of these races would be competitive. The Democrats now have a 34-19 advantage in seats (64%) of the total; if these districts were drawn in a bi-partisan manner the ratio might be more like 55% / 45% or 29-24 Democrats vs. Republicans. Not only would the ratio change, but the TYPE of winners would change - candidates on the far left or far right would be knocked out (because either they'd lose in the primary or the general election) and candidates that could reach ACROSS party lines would be likely victors.
Not only would the results be up in the air, but interest would skyrocket. Today since most people know results are pre-ordained only the die-hards bother to vote in the primaries and general election. If these seats were up for grabs (so to speak), then people would have an incentive to vote.
Finally, if California did it, it is likely that the rest of the nation would ultimately follow, since California carries significant weight. The interest in elections and type of legislator that would emerge (practical, middle of the road) would force the respective parties to fall in line eventually. After all, this model doesn't "hurt" either party if it is broadly applied; they just need to work to win over voters instead of focusing on disenfranchising voters by drawing districts to ensure that 40% or so of the voters don't even matter.
In Illinois, my district is represented by Danny Davis, who doesn't even ATTEMPT to represent River North - see here for an analysis of his newsletter, and here is a link to our gerrymandered district. Even though Illinois is pretty balanced in terms of Democratic and Republican representatives, the districts are (mostly, with a couple of exceptions) non-competitive and totally drawn to favor one party over another. I frankly don't even bother to vote in the election since Davis is a "sure thing". But I would certainly care if we had a choice between a moderate on either party...