Most representative constitutional governments established in the aftermath of our own experiment in the United States have eschewed those idiosyncrasies of our system owing to the Founders' facile anti-partisan fetish and implemented parliamentary systems instead -- and very much to their benefit for the most part.
Basic administrative functions (like raising the debt ceiling, filling key posts in a timely way) should be professionalized. The Senate Leader and House Speaker should be of the party of the Executive, and (if necessary, multiparty, multifaction) coalitions should form to support the implementation of the policy platform in the service of which the Executive are elected, else the government has no confidence. Of course, here in the United States, none of this is likely ever to be.
Given our present thoroughly institutionalized party duopoly, it is unclear that the organized and by now thoroughly anti-democratic force of the GOP can be sufficiently marginalized even in a conspicuously diversifying, secularizing, planetizing polyculture to be circumvented in a sufficiently timely and sustained way for majorities seeking to address urgent and obvious common problems -- socioeconomic precarity, climate and pandemic catastrophe, global conflicts exacerbated by global trafficking in military weapons, any one of which threaten the struggle for civilization (which I define as sustainable equity-in-diversity) and in combination threaten still worse.
"Divided Government" is dysfunctional, depressive of participation, and confuses the necessary of assignment of responsibility for policy outcomes. It seems to me that the various Golden Ages of bipartisan co-operation celebrated by Village pundits were mostly periods in which the great evil of the slave-holding and then segregated South were marginalized through their distribution into and management by both parties -- a strategy that never worked well (and could prevent neither a Civil War to resolve the question of slavery nor the betrayal of Reconstruction in the establishment of Jim Crow) and has worked ever less well during the generational "Great Sort" of the Parties in respect to white supremacy from the New Deal coalition through the Civil Rights era to the Southern Strategy and the descent into the Summers of Tea and the Winter of Trump.
It seems to me that the Founders' celebration of a hyper-individualist conception of "public happiness" informed by the specificity of their experience of Revolutionary politics undermined their appreciation of forms of other more democratic dimensions of public happiness connected to assembly, administration, organization, loyalty. (The guardian angel of this blog, Hannah Arendt, the phenomenologist of political power, elaborated the Founders' experience better than anyone, and perhaps shares some of their blind spots.) Their abstract commitments were implemented in Constitutional doctrines that have articulated progressive historical struggles in the United States. The Founders were wrong and we're stuck with their mistake.
And we ARE stuck with it: much like quixotic third-party fantasies, in which the politics to create a viable third party to solve certain very real pathologies of our duopoly are harder to achieve than to solve those problems through and in spite of the duopoly, so too the politics to create a parliamentary system to solve certain very real pathologies of the anti-factionalist quirks of our Constitution are harder to achieve than to solve those problems through and in spite of the quirks of our anti-factionalist Constitution.