It would be a monumental failure for at least three reasons:
1) The military infrastructure (facilities, qualified instructors, etc.) no longer exist because of various BRAC rounds, and would take years to rebuild.
2) Congress would have to act on multiple legislative fronts, authorizing increased troop levels across all branches, bigger defense budgets, and new military construction programs, as well as the implementation of selective service partial mobilization itself. How many votes are in Congress right now that would do all of this?
3) The political climate in this country is so divided and hot that 2023 compared to 1968 makes the latter look all peaceful and serene. Can you imagine the size and intensity of the Code Pink/anti-draft protests and riots that would erupt overnight if even a partial-draft was implemented? How many of today's Generation-Z would even show if called up for service? And how many would head for the Canadian border? The patriotism necessary for such an action, that was taken for granted in decades past, is just no longer there in the last 2-3 generations.
In 1973, the draft was abolished with the establishment of the all-volunteer force, driven largely by the American public's weariness with our debacle in Vietnam;
So how is today's public any less weary from the more recent debacles in Iraq and Afghanistan, in which it would even re-consider compulsory military service? And YES, the Biden Administration, and future administrations, would almost certainly carve out exemptions for favored protected-class and elite people, leaving the burden on lower-class rural folks and Asians and Latinos.