Telling someone they can't bring something with them into the chamber wouldn't be putting up an obstacle to entry. It doesn't require any action to not bring something.
This might be a better example. The House could likely forbid members from bringing guns into the chamber. However, could they require members to be armed? If you require members to carry firearms, you are requiring them to take an action and so are putting up a hurdle they must jump to gain entry. The Constitution doesn't grant Congressional leadership the power to impose additional requirements on elected Congressmen.
Ultimately, there's probably a line that would be drawn by the courts. I suspect that metal detectors would be allowed as the burden is so minimal that it's not much of an obstacle. The Courts are also reluctant to interfere with the inner workings of Congress. There would, however, be a limit (and a low limit at that) as to what could be required of a Congressman to gain entrance to the chamber.
This is why I never said the argument against metal detectors is the best argument or a winning argument. There is, however, a legitimate argument against requiring Congressmen to go through them.