Sens. Rand Paul, R-Ky., and Ted Cruz, R-Texas, are gaining momentum against potential rivals for the 2016 Republican presidential nomination, according to Public Policy Polling.

PPP surveyed 1,748 voters between July 19 and 21. The margin of error was +/- 3.5 percent for the general election, +/- 4.3 percent for the Republican primary and +/- 4.7 percent for the Democratic primary.

Paul has taken the lead from Sen. Marco Rubio, R-Fla., who had been leading the PPP surveys since December 2012 but plummeted to sixth place in the current poll. Rubio's fall came at the same time as he was prominently leading efforts to gain passage of the Senate immigration reform bill.

Paul comes in at 16 percent, up from 5 percent at the beginning of the year, putting him at the top of the contenders for the first time. Paul is followed by former Florida Governor Jeb Bush, New Jersey Governor Chris Christie and Wisconsin Rep. Paul Ryan - all at 13 percent.

Next comes Cruz with 12 percent, up from 7 percent in May, the biggest increase in the poll. Just 10 percent of the respondents chose Rubio as their top pick, down from 21 percent or 22 percent in the polls between January and March prior to the immigration debate.

Former Pennsylvania Sen. Rick Santorum and Louisiana Gov. Bobby Jindal each came in at 4 percent. New Mexico Gov. Susan Martinez rounded out the list with 2 percent.

Cruz leads amongst those who describe themselves as "very conservative," 20 percent to Paul's 18 percent. Christie leads amongst self-described "moderate" Republicans with 24 percent, and Bush leads amongst responders identifying themselves as "very liberal," at 50 percent.

Surprisingly, 19 percent of "very liberal" respondents chose Cruz, although that could be due to a belief he could not win against a Democratic opponent.

In a head-to-head matchup with Democratic front-runner Hillary Clinton, Christie was closest to the former Secretary of State, 43-42 percent. Paul Ryan trailed Clinton 46 percent to 44 percent, and Bush trails 44 percent to 41 percent. But all three are within the margin of error. Rand Paul, however, loses to Clinton 47 percent to 39 percent. The survey did not ask about a race between Clinton and Cruz.