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If we look at data from entrance and exit polls for a slew of early states (as reported by CNN), you can see that Trump did as well or better with Republicans than he did with independents in 11 of the 13 states below. In only two, South Carolina and Arkansas, did he do better with independents.

In other words, Trump would have done just as well in those states if no independents had voted. In fact, in a place like Alabama, he would have done better if no independents had shown up.

And then there's Nevada. It, too, was a closed caucus. And Trump won by a wide margin.

It's clear that Cruz has done better in states that are holding closed caucuses, but it's not necessarily clear why.

It is not the case, though, that Trump is leading in the contest for the nomination because he's being pushed there by independents. Trump's claim that he's bolstering the Republican Party may be exaggerated, but it's clear that an awful lot of Republicans want him to be the party's nominee.

As much as other members of the party may not like it.