House members are traditionally sworn in en masse by the Speaker of the House on the House floor during the first day Congress is in session. In 2005, Congressmen were just asked to raise their right hand. C-SPAN's
video of the event doesn't appear to show many hands on Bibles - there's simply not enough space on the House floor for every Congressman to have an aide or family member hold the Bible.
House members sometimes have ceremonial one-on-one "swearing in" photo-ops in the Speaker's office after the main event. That's the only time you'd likely see Ellison "swearing" on the Koran.
A little solid info spoiling the hysteria.
There are Jews in congress...I assume they use an Old Testament, if anything. I think Quakers affirm, not swear.
Tempest in a teacup (too small to be a teapot)