The very idea of a bipartisan commission to investigate the insurrection of 1/6/21 is grotesque, so I won't blame Rep Kevin McCarthy for opposing it... though for different reasons. It has to be noted that McCarthy, when the MAGA mob was storming the Capitol, begged Trump to call them off, and was rebuffed. Similarly, Georgia rep Andrew Clyde, who was barricading the House chamber on 1/6, recently claimed that the insurrection was no different than a normal tourist visit.
There's no need for a bipartisan commission, the Republicans are attempting to gaslight a public that knows what it has seen played over and over on numerous video streaming platforms. They would only obstruct and obfuscate. Meanwhile, insurrection instigator Rep Greene (R-8Chan), is claiming that the incarcerated insurrectionists are being abused, merely by being incarcerated. Of course, the fact that these creeps are armed, dangerous, and unrepentant doesn't even enter into her cri du cul.
To nominate a commission composed of members from both parties, the party of individuals who faced death and dismemberment at the hands of MAGA minions, and the party of individuals who egged those violent coup kooks, would be a waste of time and effort. This is a matter for the Department of Justice, and any congressional investigation would best be conducted solely by Democratic House members. No need to proceed with a charade involving known liars trying to score partisan points.