The Bush administration’s assertion that a lasting cease-fire between Israel and Hezbollah can occur only if Israel is allowed to first kill enough members of Hezbollah reflects its actions in Iraq. There too it believed that by hunting down, in Defense Secretary Donald Rumsfeld’s words, “pockets of dead-enders,” it would rapidly lead to the end of fighting.

During the first year of fighting there, the administration’s story evolved to include terrorists crossing over from Syria. But not until after a major CIA review of the insurgency did it concede the resistance was much larger than had been estimated and that it was growing from within Sunni Iraqi populations and from nationalists who objected to the occupying force and many others who had been hurt in some way by coalition forces. The number of people willing to fight the coalition is now recognized nearly as infinite, with weaponry to match.

The least-surprising story in the fighting between Israel and Hezbollah is that Arab sympathies are turning more toward the terrorist political party. Some small fraction of that support will become the next wave of fighters for Hezbollah, suggesting that the more Israel sends missiles into Lebanon, the less likely a cease-fire will be long lasting. Or it will last only long enough for Hezbollah to reorganize.

This is not to excuse Hezbollah, which provoked this war by killing Israeli soldiers and kidnapping others. But the sympathy for Israel in this situation has now largely disappeared and every day that passes and its incursion into Lebanon remains stalled, Hezbollah finds new hope and, apparently, new supporters. President Bush and Prime Minister Tony Blair are correct that Hezbollah’s is creating a more violent, less stable Middle East, but their solution of allowing Lebanon to be turned into rubble will not improve matters long term.

Any role for the United States is limited because its credibility is limited. The president’s support for a multinational force to stop the fighting and allow Lebanon’s military to gain control of its south is encouraging but the plan lacks details. Certainly, a replication of the coalition in Iraq is not sufficient.

Analysts keep pointing to 9/11 for the unexpectedly strong response from Israel, and that may be so. But another lesson is Iraq, where bombings by insurgents have increased and the world’s sympathy for the carriers of democracy has evaporated.