His statement, in preparation for today's scheduled Senate Judiciary Committee hearing on the amendment, could be seen as a thinly veiled slap at Utah's other Republican senator, Bob Bennett.
Bennett opposes amending the Constitution but is the leading sponsor of a bill that would prohibit flag desecration.
Hatch said he doesn't see flag burning as a protected form of speech under the First Amendment, as is argued by Bennett and others who back a statutory fix.
"If the First Amendment rights are to be protected, why would they want a statute that takes away First Amendment rights?" Hatch asked. "There's only one answer to that. To cover their behinds, so they can say, 'Well, I'm for a statute.' Well, that's just the usual dodge that people give when they don't want to stand up and vote for something."
But Bennett defends his stance as a principled one that puts his loyalty to the Constitution first.
"I think it is a demonstration that I am upset about people who burn the flag, but I took an oath to uphold the Constitution, not the flag," Bennett said.
Hatch believes there are 66 senators firmly committed to voting for his proposed constitutional amendment - just one short of the two-thirds majority needed to send it to the states for ratification.
Bennett said he is holding firm regardless if his vote made the difference.
"Why amend the Constitution to solve a non-problem? The only time anyone burns any flags is when this gets offered, and they burn a flag in protest of it," Bennett said Wednesday. "I'm very comfortable in where I am, and I'm going to stay there."
That leaves amendment supporters fishing for another senator. Some have focused on Sen. Robert Byrd, D-W.Va., who supported the amendment in the past but has recently changed his stance.
Sen. Sam Brownback, R-Kan., told a gathering of about 75 members of various veterans' groups that they needed to push Democratic senators to support the measure. Without backing from the minority party, it likely will not pass, he said.
"The American flag deserves every protection that we can afford, and I assure you that under my leadership this Congress will do everything it can to protect it," said Senate Majority Leader Bill Frist, R-Tenn.
Thomas Bock, national commander of the American Legion, said a statute wouldn't offer any more protection against flag burning than the laws the Supreme Court struck down in 1989. And, he insists, protecting the flag is indeed an important issue.
The amendment would not ban flag burning. Instead, it would give Congress the power to restrict desecration of the flag - a move made necessary by a 1989 Supreme Court ruling that said flag burning was a protected form of free speech.