It would have escalated the war significantly and precipitated direct Chinese intervention. The US did not go to Vietnam to fight a million Chinese (had enough of that in Korea), they simply intended to contain communist expansion, not fight WW3 over South Vietnam.
As Ozzy points out many US Generals looked at the Vietnam conflict within the context of their experiences fighting conventional battles in Korea. They assumed (and hoped) early on that at some point the regular NVA would sweep south backed directly or indirectly by China and/or Russia. They failed to take into consideration, or listen to what was happening in Malaya (even though the Brit's sent a technical team to Saigon early on).
For this reason they advocated the transformation of the ARVN from a light counter insurgency force into a heavy conventional army. The hope being that these troops would meet any invasion from the North head-on in a conventional struggle supported by US advisors, equipment and airpower. This approach ultimately reduced the fighting ability of the ARVN who became more rigid and less enthusiastic about deploying into the jungle using creative light infantry tactics.
As the war developed and the conflict started to mimic Mao's asymmetrical philosophy of swimming in your enemies sea, the black and white nature of conventional fighting turned very grey. Consequently why then bomb North Vietnamese cities to ashes if a large proportion of your enemy is fighting in your own backyard or moving through adjacent 'neutral' countries to gain unrestricted access to your home turf?
Such a policy would have alienated the US public even quicker. The media would have had even more of a field day showing pictures of burning towns and fleeing children covered in Napalm.