They have not done so. Presumably that is in part because the city's plight dictates that MPs mute the normal level of political noise and because those MPs see some real value in a bipartisan approach.
That suggests Labour's offer is not a hollow gesture.
It is, however, an offer that many politicians would refuse.
Politicians may well wax lyrical about the desirability of reaching an all-party consensus on this or that. But consensus requires compromise. Politicians do not like to find themselves shackled by the constraints imposed by being party to consensus decisions. And the suspicion remains that Governments only talk of seeking consensus-style solutions when the political cost of going it alone is too high.
When it comes to durability, the track record of such arrangements is consequently not that good.
No doubt Labour felt it was being used in just such a fashion by John Key this week as he sought cross-party backing for special legislation to overturn the Supreme Court ruling against the covert use by the police of video cameras for surveillance.
With the Maori Party and the Greens implacably opposed to the emergency measure on civil rights grounds and Act wavering, National needed Labour's votes to rush a bill through Parliament under urgency before the House rises for the election at the end of the week after next.
However, Labour did not take kindly to the Prime Minister going public and trying to blackmail it into voting for the bill by insinuating Labour would be seen to be "soft on crime" if it refused to do so.
Labour is worried about being seen in that light. But it is also wary of exposing itself to criticism on its left flank and giving liberal-minded voters another reason to jump ship to the Greens.
But Labour is not the only party in a bind however. The Supreme Court ruling has highlighted Act's long-running folly in stark fashion.
A party which holds individual freedom and civil liberties to be sacrosanct was one day bound to find those principles in direct conflict with the party's populist tough talk on law and order.
If Act ends up voting for the bill beyond the first reading stage - Act's current limit - then the pressure goes off Labour to a degree.
Labour's difficulty is that - unlike the Greens - it backs the police using covert video surveillance to gather evidence.
While it finds fault with the powers in the emergency legislation and the manner in which that legislation will be rushed through Parliament, Labour would be making a big call going into the election campaign if the bill fails because Labour refused to back it.
As of yesterday, the stand-off was continuing. Political logic suggests there will be strenuous efforts behind-the-scenes to reach a consensus which allows everyone to save some face.
Just as National and Labour are not that far apart on covert video surveillance when it comes to rebuilding Christchurch, they are also closer together than they would like to admit.
The argument for a genuine bipartisan approach to raising Christchurch from the dust and rubble was given more fodder the day after Labour's policy was announced with the news that the possible bailout of AMI Insurance could cost taxpayers more than $330 million.
National and Labour essentially agree that the reluctance of insurance companies to cover the rebuilding of homes and offices means the Government may well have to become the insurer of last resort. National is not ruling that out.
Labour is reserving the right to intervene, though stressing it would be as a very last resort.
Nine weeks out from an election, however, both parties are going to highlight their different approaches rather than talk about matters on which the largely agree.
Moreover, having shut Labour out of the picture thus far, National is not about to share any kudos it has got for its handling of the aftermath of the quakes.
Instead, the governing party has zeroed in on the extra spending in Labour's recovery package, notably the purchase of 1500 "affordable" sections.
National is also questioning Labour's promise to compensate homeowners in the red zone who undertook renovations since the 2007 Government valuations of their properties - the benchmark for compensation payments to those whose homes are now uninhabitable.
National says Labour's splurge of an extra $330 million speaks for itself in terms of that party's supposed commitment to fiscal restraint.
Labour's rebuttal is that the bulk of that money will come back to the Government as the sections are progressively sold off.
What is brazen is Labour's stealing a march on National by addressing the two aspects of the Government's compensation package which have angered red zone homeowners - the affordability of sections on which to build their new homes and the discrepancy between rating valuations and market value.
At the end of the day, however, it was just as vital for Labour's election hopes that it came up with something different from National.
Being National-lite is not going to be a winning formula.
Likewise, the need to differentiate yourself from opponent is also a clue as to how National would respond to that Labour offer of bipartisanship.
