Fresh from his victory in the Puerto Rico primary where he collected all 23 delegates at stake, Sen. Marco Rubio received another piece of good news on Monday: A new poll showed that he has significantly cut the lead of Republican presidential front-runner Donald Trump in Florida, which holds a winner-take-all primary on March 15, Newsmax  reported. The winner of that contest gets all the state's 99 delegates.

In the Monmouth University survey released Monday, Trump is leading Rubio by 8 points—12 points down from the 20-point advantage that Trump had over Rubio just last month, based on three surveys.

In the latest poll, Trump has the support of 38 percent of the voters in Florida, Rubio has 30 percent, Texas Sen. Ted Cruz, 17 percent; and Ohio Gov. John Kasich, 10 percent.

Moreover, according to the new poll, Rubio leads Trump among the approximate 1 in 5 voters who have already cast their ballots, 48 percent to 23 percent.

"Rarely will you hear a poll called 'good news' for a candidate when it has him down 8 points in his home state, but this really is the most encouraging news Rubio's had in ages," the website HotAir.com writes in a commentary.

The commentary says Rubio's impressive lead in the early voting is "way, way off from what most people expect."

"It's Trump who's supposed to be cleaning up in the early vote, not Rubio," HotAir.com writes. "Trump's the one who's been leading in the polls there for months and Trump's the one with the most enthusiastic voters. If anyone's banking votes early, you'd expect it to be him."

However, Trump still leads among those who haven't voted yet, 42 percent to 26 percent, according to the new poll.

In a hypothetical head-to-head vote between Trump and Rubio in Florida, Trump still wins over Rubio 47 percent to 45 percent, according to the poll.

But with still a week before March 15 and with momentum on Rubio's side, a win by the Florida senator in his home state is still considered a distinct possibility.

"Rubio is within shooting distance in his home state with a week to go in this volatile nomination contest," Patrick Murray, director of the university's Polling Institute said in a statement.

The poll's margin of error is plus or minus 4.9 percentage points.

Meanwhile, Rubio's campaign spokesman is vehemently denying a CNN report that some of the senator's advisers had advised him to quit the race before his home state votes on March 15.

CNN reported on Monday that while Rubio is "bullish" on staying in, some of his advisers have expressed fears that a loss in Florida could hurt Rubio politically not only in the short-term, but farther down the road.

The CNN report was "utter nonsense," Rubio communications director Alex Conant told CNN's Wolf Blitzer.