But Cruz’s ballot-test numbers aren’t the only ones that don’t look great for him — or perhaps more accurately, aren’t as good as you might think. No, you also could make a pretty strong argument that Cruz’s take-no-prisoners style (on display during the 2013 government shutdown) has alienated plenty of Republicans, too. And overall, his national brand is a little less sterling than you might think for a supposed conservative hero.

This has been shown in a few different polls. To wit:

1) An NBC News/Wall Street Journal poll released this month showed that 38 percent of Republicans said they couldn’t see themselves backing Cruz, with 40 percent saying they could support him. The only other top-tier candidate with a worse ratio of potential supporters to non-starters was New Jersey Gov. Chris Christie (32 percent to 57 percent), whose issues with the GOP base are well-established.

More: Ted Cruz Is a Conservative Icon. but Plenty of Republicans Don’t Care for Him.