I'm not sure what kind of constitutional issues such a requirement would raise. But to be clear, the suggestion is not that the justices behave as partisans, but that they be appointed by partisans.
They're *already* appointed by partisans though. Anyway, I did not think that your suggestion was that justices must act in a certain way, my point was that some alarm bells should be going off when we are talking about codifying an ideological balance/deadlock. When I used the word principles I was talking more generally in terms of what the Constitution represents, not that it explicitly bars such a proposal (though Art 2 Sec 2 would seem to run counter to your particular solutions, at least in spirit). The Supreme Court was never intended to be foremost an abstractly fair or unbiased body, it was intended to be a final and decisive adjudicator above all else.
And here's a simple suggestion for how the rule could be implemented: the Senate changes its rules such that they won't consider a Supreme Court nominee who isn't supported by a majority of Senators of the party that "controls" the seat to which the nominee is nominated. Alternatively, the rules could provide that the Senate won't consider the nomination of a Supreme Court justice who is not one of a handful of potential nominees chosen by majorities of the appropriate party.
The number of holes and inconsistencies with this kind of "solution" is immeasurable. Again, the stated motivation for this proposal is to prevent partisan actors from screwing up an intentional deadlock at the Supreme Court. That means you have to presume that partisan actors will work to circumvent the deadlock, so your solution has to be able to stop bad actors. But your solution is contingent on the non-existence of the very problem we're trying to solve.
Even putting aside the problem of why partisan actors would enact rules and policies that would prevent them from acting in a partisan fashion, how does this even prevent those actions in the first place? First, we have the problem that they're rules and not laws. So any future Senate majority can simply erase them. Second, we have the problem of how to define the relationship between parties and nominees. Who "owns" Kennedy's seat and how do we resolve a dispute over that ownership? Is the balance of the court determined by the ideology of the actual Justices or the ideology of the parties in the Senate? The latter does nothing to stop the Justices from being unbalanced, and the former doesn't resolve candidates whose ideologies are not easily classified.
Hell, what happens if the future makeup of the Senate is neither Democratic nor Republican because of the formation of new political parties? Do the few remaining Democratic and Republican Senators get to decide who can be considered for Supreme Court positions because they "own" them? How do we even handle the emergence of a new political party in terms of ideological balance? Do we have to expand or shrink the court and make each party have equal representation? How large does a party have to be in order to merit ownership of a Supreme Court seat? Does the Tea Party get a distinct seat separate from Republicans in general?
Next, you say "consider" instead of "confirm". So let's say Justice Thomas dies and Democrats control the Senate but Republicans control the Presidency. The Democrats could conform to these rule and "consider" a Republican nominee, then simply refuse to hold a vote, or to hold a vote and refuse to confirm. So we'd basically be in the situation we're already facing where the Senate does nothing and the balance of the Court changes on its own.
And what about the nominee themselves? Suppose the Republican president wishes to appoint a Justice who the majority of their party in the Senate does not support but whom a majority of Democrats would support. Are we now going to say that the Republican president should be prevented from nominating the candidate of their choice because the majority of the Senate minority opposes it? How do we reconcile such rules and complications with the President's explicit power to nominate in Article 2 Section 2? Such Senate rules would be a clear encroachment on said right even if they don't directly interfere with it.
One more example as I could keep going on and on. Say the minority party or the party who owns the vacant seat supports a nominee who otherwise disturbs the deadlocked balance, that is, the President puts forward a liberal/conservative justice that would put the court at 5-3. What mechanism do we have in place to prevent a stupid or naive party from unbalancing the court?
Well, I suppose that's the trouble with debating imaginary versions of real people.
The fact that this proposal is only being discussed in the wake of Scalia's death is not imaginary. Knowing your historical viewpoints and posting patterns and the fact that you have never brought up such an idea in this community in all these years despite your focus on Supreme Court related subjects is not imaginary. That you give no serious analysis to the problems associated with actually enforcing such a solution is not imaginary (putting aside the issue of enacting it). I go back and forth on giving you the benefit of the doubt a lot of the time, but you burn those inclinations more often than not.