Per the polls so many believe in, Trump was first or second choice of voters during the primary. So yeah he had the most approval of any GOP candidate. As well as the most votes ever in a republican primary. So yeah majority.
Which primary? Oh, the poll you cite
http://talkingpointsmemo.com/polltracker/cnn-donald-trump-leads-august is from
2015 Maybe he had that support in Iowa, maybe, but after that, he'd gone from second choice to last place with me. And he continued to shed support rapidly with other conservatives.
Per Political after all the heroic effort of the Cruz team to stack the Convention rules committee with #neverTrump people, there are only 6 out of 112 on it that agree with the anti-trump people. Logically since that was the most effort one, and allowing for the same effort with the rest of the delegates its stands to reason, MOST Conservatives at least delegates do not agree with the anti-Trump crowd.
So yes, I can say with reasonable degree of certainty that the anti-Trumps are not the majority of conservatives.
Are you using Conservatives or Republicans for your little study group?
It has been an item of note for a few election cycles that Republican does not equal Conservative. If you are polling Republicans, you have watered down the Conservative response, judging by the primary vote, by at least a factor of two.
If you are including the people who are so desperate to keep hillary out of office they'd sell their soul and vote for the donald, you have watered down the conservative response, although there may be those who honestly think electing Trump would matter very much. Considering the two are longtime cronies, I have serious doubts there would be a significant difference with the exception of relegating the GOP to the dustbin of history.