"Each candidate for nomination for the president of the United States and vice president of the United States shall demonstrate the support of a plurality of delegates from each of five (5) or more states, severally, prior to the presentation of the name of that candidate for nomination," RNC Rule No. 40 reads.

Gingrich has only won two states so far — Georgia and South Carolina. But Hammond said there were "plenty of states left for us to pick up three wins," saying he thought Gingrich could have strong showings in states like Kentucky, West Virginia, Maryland and Texas.

Gingrich could also hunt for delegates from states who do not formally bind their delegates to the result of their primaries and caucuses, including Iowa, Pennsylvania, Maine, Minnesota, Montana and North Dakota.

And while the rule could deal a blow to the optics of Gingrich's bid for the GOP nomination, practically, Gingrich has little chance of capturing the 1,144 delegates to win the nomination on a first ballot. If front-runner Mitt Romney falls short of the magic number as well — the strategy both Gingrich and Rick Santorum have said is their goal in remaining in the GOP primary — subsequent rounds of voting could open up to all candidates.