A method of treating viral infection of mammalian cells by an Enterovirus or Rhinovirus, comprising exposing host cells to an effective amount of an antiviral compound that comprises a morpholino antisense oligonucleotide of between 15 and 25 morpholino subunits having a substantially uncharged, nuclease-resistant backbone containing phosphorodiamidate intersubunit linkages joining a morpholino nitrogen of one subunit to a 5′ exocyclic carbon of an adjacent subunit, wherein the morpholino antisense oligonucleotide comprises a targeting sequence of at least 15 nucleotide bases complementary to SEQ ID NO:7 and, conjugated to the morpholino antisense oligonucleotide, an arginine-rich polypeptide effective to promote uptake of the antiviral compound into the host cells, wherein the arginine-rich polypeptide has the sequence of SEQ ID NO:15.