So since you don't like the current partisan make-up of the Senate, it should be abolished? Maybe we should abolish the House....Except how it functions has changed for partisan reasons.
The only reason the government is "shut down" is because Republicans in the House would not fund Obamacare, for which Democrats then decided to shutdown all of government instead. The Senate could have easily just passed financing everything else. The same is happening in relation to the debt.
The "change" that has come is the media and public perception that if one aspect of government doesn't get what it wants, then all of the government and economy must be shut down. This is a radical shift in the perception of how Congress and the budget works. Until now, how it worked was everything that was agreed upon was paid for and everything else was not. Now it is that everything must be paid whether there is agreement or not, and if everything isn't paid for then nothing is paid for. And the media and public have (bizarrely in my opinion) accepted that practice.
The potential "gridlock" used to be fully functional because it meant everything agreed upon was done, and only what was not agreed upon was "gridlocked." NOW, any disagreement shuts everything entirely down at huge economic and national danger. Thus, gridlock is no longer tolerable to allow.
All that, of course, by passes the one-citizen-one-vote issue.
But for your point, gridlock potential has shifted from being a safeguard to perpetual extortion and playing Russian roulette. The role of Congress in terms of budget has been 100% diametrically reversed. That reversal is supportive of an Imperial presidency if the president is of the same party as either half of Congress. Simply, the actual power of Congress has been stripped away, leaving a void and the chaos that can bring.
Your message is no longer accurate. It is not that the government won't do what it doesn't agree on. Rather, to the government won't do anything unless everything is agreed upon. That is a diametric opposite of past practices and I believe the intent.