Part of this is from memory, so it's suspect. Jesse had a radio talk show before he ran for governor, and he regularly talked about firearms, mostly military stuff, and how the government should not restrict gun rights.
Then he got elected, and his attitude changed about 179-degrees. There was some fuss after he initially was denied on his CCW, but his concerns ended at the tip of his nose. When he was in a position to make a difference, he did nothing to promote gun rights and I actually have the impression he did not want a CCW bill to pass. If Series 70's recollection is more complete than mine, I suspect the language he insisted on was something he knew would never pass.
Now that he's got his own show again (which is itself a joke: it was supposed to be 5 nights/week but he was so bad MSNBC delayed it about 6 months and then made it once weekly, and the debut got a worse share rating than Aunt Emma's Sewing Tips, or something like that) I'm not the least bit surprised he's playing to his preferred image, rather than to his reality.
Here is a thorough, unedited, and complete list of everything Jesse cares about: (1) Jesse, (2) money (see #1), and (3) maybe his family, so long as it doesn't interfere with #1.