There are enow of zealots on both sides who kindle up the passions of their partizans, and under pretence of public good, pursue the interests and ends of their particular faction. For my part, I shall always be more fond of promoting moderation than zeal; though perhaps the surest way of producing moderation in every party is to increase our zeal for the public. Let us therefore try, if it be possible, from the foregoing doctrine, to draw a lesson of moderation with regard to the parties, into which our country is at presentg divided; at the same time, that we allow not this moderation to abate the industry and passion, with which every individual is bound to pursue the good of his country.
Those who either attack or defend a minister in such a government as ours, where the utmost liberty is allowed, always carry matters to an extreme, and exaggerate his merit or demerit with regard to the public. His enemies are sure to charge him with the greatest enormities, both in domestic and foreign management; and there is no meanness or crime, of which, in their account, he is not capable. Unnecessary wars, scandalous treaties, profusion of public treasure, oppressive taxes, every kind of mal-administration is ascribed to him. To aggravate the charge, his pernicious conduct, it is said, will extend its baleful influence even to posterity, by undermining the best constitution in the world, and disordering that wise system of laws, institutions, and customs, by which our ancestors, during so many centuries, have been so happily governed. He is not only a wicked minister in himself, but has removed every security provided against wicked ministers for the future.
On the other hand, the partizans of the minister make his panegyric run as high as the accusation against him, and celebrate his wise, steady, and moderate conduct in every part of his administration. The honour and interest of the nation supported abroad, public credit maintained at home, persecution restrained, faction subdued; the merit of all these blessings is ascribed solely to the minister. At the same time, he crowns all his other merits by a religious care of the best constitution in the world, which he has preserved in all its parts, and has transmitted entire, to be the happiness and security of the latest posterity.
(David Hume, Essays, Moral, Political, and Literary, "That Politics May Be Reduced to a Science," paragraphs 14-16.)
Hume's solution to the problem of partisanship is to respond by pointing out that neither side is acting in a manner consistent with the constitutional principles they profess to uphold: if the principles are good, there is no reason to think the minister's replacement is so very urgent that it must be done now, and if they are bad, it makes no sense to attack the minister for not preserving them; if the principles are good, there is no reason to think the minister's being in power is so very important that it will be horrible if he is replaced, and if they are bad, it makes no sense to praise the minister for preserving them for posterity.
I doubt that this would actually be successful in general, although it might be a start for something.