Kentucky Sen. Rand Paul moved in the opposite direction over the same period, with the share of likely GOP primary voters who said they could see themselves backing him falling from 59% in late April to 49% in mid-June. The decline came as Mr. Paul battled fellow Republicans over his effort to end the National Security Agency’s bulk collection of phone records.
The Journal/NBC News survey, conducted from June 14 to 18, found that the fortunes of a number of Republican White House hopefuls have shifted since the April survey, a period in which a dozen major Republicans declared their candidacies and began formally introducing themselves to voters. Four additional candidates, all sitting governors, are expected to enter the race soon.
The changing views on the candidates were most pronounced for some of the second-tier contenders. Support for the three leading candidates— Jeb Bush, Scott Walker and Marco Rubio—largely held firm, a potential sign that voter perceptions of each are starting to solidify.
Potential support for Mr. Bush, a former Florida governor, edged upward, with the share of Republican primary voters who said they were open to his candidacy rising to 75% in June from 70% in April and 49% in March.
Mr. Walker, the governor of Wisconsin, slipped slightly, while support for Mr. Rubio, a Florida senator, was unchanged. Of the three, only Mr. Walker hasn’t yet declared his candidacy. His announcement is expected in mid-July.
More results from the Journal/NBC News poll will be released Monday.
The biggest movers in the new survey were Ms. Fiorina and Messrs. Carson and Huckabee.
The share of Republican primary voters who said they were open to supporting Ms. Fiorina, a former chief executive of Hewlett-Packard Co., jumped from 17% in April to 31% in June, about even with the 29% who said they weren’t open to supporting her.
The number of Republicans who said they could support Mr. Carson, a former pediatric neurosurgeon, and Mr. Huckabee, a former Arkansas governor, grew by 11 and 13 percentage points, respectively. All three formally entered the race in early May, just after the April poll.
The other Republicans to enjoy a noticeable bounce in between Journal/NBC News surveys were former Texas Gov. Rick Perry, whose tentative support grew by eight percentage points, and former Pennsylvania Sen. Rick Santorum and businessman Donald Trump, who both saw nine percentage-point bumps.
The bad news for Mr. Trump is that two-out-of-three Republican primary voters said they wouldn’t consider voting for the reality-television star and real-estate developer, whose announcement this past week generated significant news coverage and more social-media discussion.
New Jersey Gov. Chris Christie also faces stiff resistance heading into the Republican nominating contest, with 55% of GOP primary voters saying they wouldn’t be open to supporting him.
Mr. Christie is expected to announce his plans in the next few weeks. The once high-flying governor has made regular trips to New Hampshire as he tries to revive his image among Republicans and independents in the first-in-the-nation primary state.
The poll of 1,000 adults had a margin of error of plus or minus 3.1 percentage points. For the 236 GOP primary voters surveyed, the margin of error was plus or minus 6.38 percentage points.