The issue is especially sensitive in South Carolina, where officials brag that no GOP nominee has been minted without first winning the state's first-in-the-South primary.
"This is about following the rules," Floyd said.
RNC spokeswoman Kirsten Kukowski said Thursday that the convention would stay in Tampa. However, states that don't abide by RNC rules face penalties, which could include losing delegates to the convention.
Traditionally, Iowa goes first, followed by New Hampshire, South Carolina and now newcomer Nevada.
Some states, including Georgia, Connecticut, Virginia, Maryland and California, have or are working to move contest dates back to no earlier than March 6.
Florida's GOP-dominated legislature hasn't budged on a 2007 state law setting that state's primary for the last Tuesday in January, or Jan. 31, 2012.
Floyd called for a task force to look at moving the convention, saying Florida is not abiding by the rules adopted by two-thirds of RNC members.
Florida's top House Republican, though, wasn't moved by Floyd's call.
"I look forward to meeting Chairman Floyd and Chairman Strawn in Tampa next summer," House Speaker Dean Cannon said.
Cannon and Senate President Mike Haridopolos have said they will consider moving Florida's primary only if it comes fifth after Iowa, New Hampshire, South Carolina and Nevada. So far, Florida's GOP-controlled Legislature has not considered changing the date.
But Floyd said a state that doesn't follow the rules shouldn't have the honor of a convention when it could be hosted in other states "that have legitimately fought the great Republican fight." During 2008's intense campaign, states scrambled to hold their primaries as soon as possible to have a say in the nomination process. That touched off threats to strip states of delegates and other penalties. Leaders in both parties agreed to require later contests in delegate-rich states.
Floyd said no matter what Florida does, South Carolina will move its primary ahead to maintain its first-in-the-South status. Iowa GOP chair Matt Strawn said Floyd was right to call for the convention to be moved.
"If Florida refuses to move its primary date into compliance with RNC rules, that consequence should be the re-opening of the process to select the site of the 2012 RNC Convention," Strawn said.
In June, the RNC chose Tampa as the convention site over Phoenix and Salt Lake City.