New poll is troubling news for Hillary Clinton if she wants to be president

(CNN) -- While Hillary Clinton still maintains an advantage over potential GOP rivals in 2016, a new poll shows that her lead is narrowing.

And as her book tour has received extensive coverage, her support has dropped below 50%, according to the McClatchy-Marist poll released Thursday.

The survey also looks at the 2016 Republican primary and who fares best among the potential candidates.

Clinton vs. Republican

In a hypothetical matchup against Sen. Rand Paul, Clinton bests the Kentucky Republican, 48%-42%, with 10% undecided. The 6-point margin is equal to the poll's sampling error, and the gap is narrower than in April, when Clinton had a 55%-39%

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Matched against Gov. Chris Christie, Clinton leads the New Jersey Republican, 47%-41%, with 12% of voters undecided. That's down from her 53%-42% advantage over Christie in April.

Clinton has also lost her wide margin over former Florida Gov. Jeb Bush, who she leads 48%-41%, down from her 55%-39% advantage in April.

Republican primary

The poll also asked Republicans and Republican-leaning independents who they would support in the GOP presidential primary. Like nearly every other 2016 poll, the McClatchy-Marist poll indicates there is no frontrunner in the race, and nearly a quarter of Republicans are undecided.

Bush and Christie tie for the top spot at 13% each, with Sen. Ted Cruz of Texas following behind at 10%. Rep. Paul Ryan of Wisconsin, who served as the 2012 vice presidential nominee, ties with Sen. Marco Rubio of Florida at 9%.

Paul and Texas Gov. Rick Perry tie at 7% each. Gov. Scott Walker of Wisconsin, former Sen. Rick Santorum of Pennsylvania, and Louisiana Gov. Bobby Jindal all receive less than 5% of support.

The poll also indicates that Paul, while trying to expand the Republican Party has lost support among tea party supporters. In April, he came in at 20% among tea party backers, with Cruz at 6%. Paul now has only has 7% support from the group, compared to Cruz at 15% - the top spot.

The survey was conducted on August 4 with 1,035 adults, including 806 registered voters, questioned over the phone. The registered voters' subset has a sampling error of plus or minus 3.5 percentage points. For questions about the 2016 GOP primary, 342 Republicans and Republican-leaning independents were interviewed, with a sampling error of plus minus 5.3 percentage points.