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By Paul Steinhauser

CNN deputy political director

(CNN) -- A new survey indicates that presidential candidate Sen. John McCain has made dramatic gains with California Republicans.

Sen. John McCain is leading in California, according to a CNN poll out Monday.

The Arizona senator is 13 points ahead of his closest rival in a CNN/Opinion Research Corp. poll released Monday: Thirty-nine percent of likely California Republican primary voters back McCain, while 26 percent support former Massachusetts Gov. Mitt Romney.

For McCain, that's a 19-point jump in the polls since the last CNN/Opinion Research Corp. survey conducted in the state two weeks ago. Romney made gains as well, rising 10 points over the past two weeks.

Since the previous poll, McCain has won the South Carolina Republican primary, which was the first test of Southern voters for the Republican White House hopefuls. Romney scored victories in Michigan, his native state, and Nevada, where he was one of the few candidates to actively campaign.

Former New York Mayor Rudy Giuliani is in third place in the new survey, with 13 percent of California Republicans backing him for the GOP presidential nomination. Former Arkansas Gov. Mike Huckabee is at 11 percent and Rep. Ron Paul of Texas is at 2 percent.

Six percent of likely Republican primary voters remain undecided. That's down from 15 percent two weeks ago.

When it comes to the issues, "Romney has a slight edge over McCain on economic matters, while McCain holds a big lead on the war in Iraq and terrorism among California Republicans," said CNN polling director Keating Holland.

The poll also suggests that a third of California Republican voters think McCain would do the best job handling illegal immigration. That's more than believe that Romney (20 percent), Giuliani (19 percent), or Huckabee (13 percent) would do the best job with that issue.

Most political observers believe McCain's standing among Republicans was hurt because of his backing of legislation that called for an eventual pathway to citizenship for some illegal immigrants. That's a stance that worries some conservatives. While he hasn't changed his position on illegal immigration, he now emphasizes beefing up border security first.

The poll is another indication of McCain's dramatic political rise from "near death." His campaign bottomed out over the summer, after running low on cash, cutting staff, and dropping in the polls. Now, after major victories in some of the crucial early primary states, he tops the national polls and his fund-raising has revived as well.

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"McCain's gains have come primarily among liberal and moderate Republicans as well as GOP voters under the age of 50," Holland said. "Among liberals and moderates, McCain's support doubled from 25 percent to 50 percent in the last two weeks. McCain also gained 29 points among GOP voters under 50 years old."

But there's a lot on the line Tuesday, when Florida Republicans vote.

A Florida victory could cement McCain's status as the GOP front-runner going into Super Tuesday one week later. A loss to Romney would leave the battle for the Republican presidential nomination wide open.

A CNN compilation of the latest polls in Florida shows McCain and Romney in a statistical dead heat for first place. And unlike New Hampshire and South Carolina, where McCain won primaries thanks to support from independent voters, Florida holds a closed primary, meaning only registered Republicans can vote in the GOP primary there.

California is the biggest prize on Super Tuesday, February 5, when 24 states hold contests. There will be 1,020 Republican delegates at stake in 21 states, 170 from California; and 1,681 Democratic delegates at stake in 22 states and one territory, 370 from California.

In the fight for the Democratic presidential nomination, 49 percent of likely Democratic primary voters in California are backing Sen. Hillary Clinton of New York, while 32 percent support Sen. Barack Obama of Illinois and 11 percent back former Sen. John Edwards of North Carolina. Those numbers are virtually unchanged from the last CNN survey conducted two weeks ago.

But it should be pointed out that more than 80 percent of the respondents were questioned before Obama's rout of Clinton and Edwards in Saturday's South Carolina primary. Those results could shift numbers in California and elsewhere.

As for the issues, "Clinton has the edge over her rivals on health care, the economy and Iraq," Holland said. "Obama and Clinton are virtually tied when likely Democratic primary voters are asked about which candidate would bring change to Washington."

The poll also indicates that 70 percent of Democrats say their vote is certain.

That number stands at 57 percent for Republican voters. The remaining 43 percent of Republicans say they might vote for someone else.

For this poll, 2,212 adults were interviewed, including 690 likely Democratic primary voters and 437 likely Republican primary voters. The survey was conducted by telephone from Wednesday through Sunday. The poll's sampling error is plus or minus 4.5 percentage points for Republicans and 4 percentage points for Democrats.