Three-quarters of GOP primary voters say they could see themselves supporting Mr. Bush or Mr. Rubio, a significantly larger share than for any other contender.

Only Mike Huckabee is close after a surge of support since the prior Journal/NBC News poll, in April, with 65% now saying they could see themselves backing him. The survey found a decline in support for Sen. Rand Paul of Kentucky.

The news is particularly good for Mr. Bush, a former Florida governor, who has weathered a mixed set of developments in recent weeks. The potential support for Mr. Bush rose slightly, by five percentage points, since April and has jumped 26 points since March.