Is it because it's so important to the Middle East? The fact is that Palestinians are a reflection of the wider Arab world, not its leaders. The path to a more peaceful and stable Middle East goes through Iraq, Iran, Syria and Saudi Arabia, all of which are a more appropriate subject of the attention of the United States than Gaza.
The line that the peace process "cannot be allowed to fail" is similarly nonsense. If the two parties aren't genuinely interested in peace, it will fail inevitably, no matter how many trips Colin Powell makes to the region. Israeli society has probably made a fundamental choice for peace, but the Palestinians haven't yet.
Peace in the Middle East only comes when the Arab side realizes violence is hopeless. Egypt was beaten in 1948, 1956, 1967 and 1973, and only then did Egyptian President Anwar Sadat decide to reach for the olive branch. Israeli military strikes against Palestinian terror are, therefore, probably a counterintuitive contribution to peace -- in the long run.
A proper understanding of the peace process -- fundamentally, it's not a responsibility of the United States -- puts the proposal to send American troops chasing Hamas terrorists in perspective: It would be a mistake. And not one borne of excessive hawkishness, but of the foolish logic of the advocates of the peace process.