They don't want a bi- or non-partisan independent commission to examine what happened. They know they couldn't attack its findings as partisan motivated since they would be involved. There's no political benefit for them in this type of investigation, an investigation which would clearly cause problems for them inside and outside the Party. The media would ask Republicans about the findings, they would be on the defensive and Trump would be going berserk complaining about the investigation and they would have to defend him or abandon him and incur the wrath of the Trumpists. So they want to let the House and Senate conduct the investigations - and the DOJ - so they can play the victim card. It may be smart politically but this is putting party over country to the extreme. Disgraceful.
McConnell said this after the attack/riot: "Former President Trump's actions preceding the riot were a disgraceful dereliction of duty... There is no question that President Trump is practically and morally responsible for provoking the events of that day. The people who stormed this building believed they were acting on the wishes and instructions of their president. And their having that belief was a foreseeable consequence of the growing crescendo of false statements, conspiracy theories, and reckless hyperbole which the defeated president kept shouting into the largest megaphone on planet Earth. The issue is not only the president's intemperate language on January 6th….It was also the entire manufactured atmosphere of looming catastrophe—the increasingly wild myths about a reverse landslide election that was being stolen in some secret coup by our now-president."
But we can't have a commission, no. Shameful.
One of the six Republicans in the Senate who voted for the commission, Ben Sasse, said this: “Nebraskans know where I stand on this: For the first time in our history, a mob targeted the Vice President and the Congress for following the Constitution by certifying the Electoral College vote. With Congress getting weaker and tribalism getting stronger, we’ve got to rebuild some public trust. Like others in the Nebraska delegation, I think that, if done right, a truly bipartisan commission could complement the work being done in the ongoing criminal investigations. The American people deserve a full account of what happened.”
Even that is too half hearted but at least it's something.