They're claiming he can't be charged unless he's impeached by the House, convicted by the Senate, and removed from office. Everyone is focusing on it he kills a political rival, but no one's thinking it through - they're acting like it'll be just one murder, but he has no impulse control.

He kills his enemies, then he kills anyone in the House who looks like they'll vote for impeachment - they may or may not need to vote in replacement Representatives. If he's still impeached, he kills any Senators who look like they'll vote to convict (again, they may need to vote in replacement Senators). If he's convicted, he can send his assassins against the people who would remove him from office.

So essentially, be gets to do what he wants until he's stopped, but he can just keep murdering Senators and Representatives until either there isn't a quorum or everyone is too scared of being assassinated for vote against him.