Nate asks: “if Obergefell is truly on the precipice, as so many Democrats are arguing — why not vote to codify it?”
One reason is that there is no constitutional mechanism for doing so. Marriage law is set by the states, not the federal government, and, under the U.S. Constitution, the federal government enjoys no power to preempt those laws. Obergefell, you will note, did not claim such a power for the federal government; it claimed that the due process clause of the Fourteenth Amendment “requires a State to license a marriage between two people of the same sex and to recognize a marriage between two people of the same sex when their marriage was lawfully licensed and performed out-of-State.” This is not the same thing as handing legislative power to Congress.
The assumption that Washington, D.C., is omnipotent is one of the biggest problems of our era. It would be an extremely bad idea for conservatives to begin taunting the Democratic Party for declining to pass federal laws that the federal government has no constitutional power to enact.