The dominance of single-member districts (SMD) for U.S. House elections is relatively new. Using proportional voting would not require a constitutional amendment. All the Constitution touches on is the apportionment of seats to each state, not how many seats will be elected from any given district. For states to have the option to use proportional systems, only statutory change is needed.
In March 2007, Congress considered legislation to extend to the District of Columbia full voting rights in the federal House of Representatives. The D.C. Voting Rights Act called for increasing the House to 437 members from 435 and granting a voting representative to the district. Because that member likely would be a Democrat, a compromise addressed questions about partisan fairness: balance the D.C. seat by adding a Republican-leaning seat to Utah, which likely would have received an additional seat following the 2010 census and reapportionment.
In doing so, without addressing Utah's district map, the D.C. VRA called for nested, multi-member district (MMD) in Utah. On March 20, 2007, the Congressional Research Service (CRS) issued a report supporting a MMD's constitutionality.
[CRS report on MMD constitutionality - PDF 65k]
[History of SMD for U.S. House races]