Donald Trump speaks at a news conference in Manhattan after he signed a pledge Thursday to support the Republican nominee in the 2016 general election. (Spencer Platt/Getty Images)

It's obvious that there is a large part of the Republican Party that would very much like Donald Trump to go away. As a corollary to that, there is a large part of the opposition to Trump that insists that he's winning because independents are tipping the scales in what would otherwise be a close contest among Republicans.

A key part of that argument derives from where Ted Cruz has won so far, including Kansas on Saturday night: Caucus and primary states in which voting is closed to non-Republicans. That was the case in Iowa, it was the case in Alaska, it was the case in Oklahoma. Cruz won them all. Why? Because it was Republicans-only, the argument goes.

There are two problems with that argument, though. The first is that Trump has been winning Republican voters in most states, or doing just as well with both Republicans and independents. The second problem is Nevada.

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.