We looked at the numbers he's referring to -- how turnout in both parties' primaries changed since their last competitive fight -- and it's true that the Republicans have seen a bigger boost in turnout this year.
But that's different than Trump "growing the party tremendously." For that to be the case, there would need to be an increase in the actual number of Republicans.
Voter registration data for New Hampshire is available through December, and it suggests that Republican registration dropped a bit over the end of 2015. But that was before the primary was imminent, so it's not a great guide.
Data from Iowa shows slight growth of registered Republicans from December to February -- a 0.71 percent increase. The number of independents increased about half as much.
We can evaluate this a bit differently, though. If we take data on the composition of the vote in the first three Republican states to vote and compare it to turnout, we can see that the density of the Republican vote in the first three states was up significantly since 2012. What's more, while the number of independents that came out to vote was fairly flat, the number of Republicans turning out was up a decent amount.
That's tremendous growth -- but not necessarily of the party.
Data from California's secretary of state, out this week, indicates that the Republican Party there is vanishing, switching over to a decline-to-state (a.k.a. independent) registration. What's happening in the states varies.
There is a national metric we can look at. Gallup surveys Americans on a monthly basis to determine their stated party identification. And since July, when Trump jumped into the race, the number of people who identify as Republican is up seven points -- to 33 percent. That's ... a tremendous growth.
It's a bit of cherry-picking. Last January, the percentage of people identifying as Republican was at 29 percent. It sank and then increased again.
But we have to admit: The evidence suggests that more people are identifying as Republicans and more Republicans are voting. The question of whether or not that is the doing of Donald Trump is impossible to answer. But part of Trump's skill in bragging is that it's often hard to disprove.
Practice makes perfect.