A new poll reveals that Hillary Clinton is within striking distance of beating Donald Trump in Texas just as voting is about to get under way.

According to the survey by CBS News and YouGov, Clinton trails Trump by only 3 percentage points among likely voters in Texas, where no Democrat has won a single statewide race in 20 years. That's within the poll's margin of error of 4.4 percentage points, meaning the race is essentially a statistical tie. You can check out the results here.

"We've been seeing polls for a number of months that have the race in single-digits," said state Rep. Rafael Anchia, a Clinton supporter and member of the Democratic National Committee. "We don't know how the last weeks of the campaign will go, but anything is possible in the state of Texas."

The poll includes voters who chose to participate in an online panel, a methodology that is considered less authoritative than traditional random-dial polls. But the results track with several other surveys showing Texas to be much more competitive than in a typical presidential year.

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The new poll shows 43 percent of Texans backing Clinton, while 46 percent prefer Trump.

In 2008, Barack Obama pulled 44 percent of the vote against John McCain. In 2012, Obama's share of the vote here slipped to 41 percent.

"We do know that Hillary Clinton will improve on what Barack Obama did in Texas," Anchia said. "You can take that to the bank."

According to CBS's "Battleground Tracker," Clinton is winning 18-to-29-year-olds by 21 points and winning 30-to-44-year-olds by 8 percentage points.

Anchia pointed out that Clinton will pound Trump with Hispanic voters, and he says if Libertarian candidate Gary Johnson does well, Clinton could win the Lone Star State without getting to 50 percent of the overall vote. Johnson is at 5 percent in the CBS poll.

Clinton's campaign hasn't shown signs of significantly investing in an effort to win the state. A recent decision to advertise here drew attention, but it was a modest buy, particularly compared with what the Democrat is spending to try to win another traditionally Republican state, Arizona. And unlike in Arizona, the Clinton campaign isn't sending prominent campaign surrogates here for events.

Early voting begins Monday. Election Day is Nov. 8.

According to the polls, Trump is having problems convincing voters that he's a legitimate candidate. Only 40 percent say he is prepared to be commander in chief, compared with 51 percent who say Clinton is.

The poll found that "voters are also more likely to say Clinton has good temperament and judgment" by a margin of 16 points. And only 35 percent think Trump respects women; more than half say he has not adequately explained his past comments suggesting that he could get away with sexually assaulting a woman because he's a celebrity.

But Clinton also has her problems, which helps explain Trump's lead, along with the structural advantage for Republicans. About 38 percent say she could fix the economy, vs. 50 percent for Trump; only 33 percent think she has explained her "past comments in emails"; and 70 percent say she is not honest and trustworthy.

Trump voters in Texas, as in other places, like his pledge to build a wall along the southern border. The polls found that 56 percent think the wall is a good idea, but only 36 percent think it can probably be completed. Past polls have found a majority of Texans oppose building a wall.

Former Dallas County Republican Party Chairman Jonathan Neerman said the outcome here "is going to be a hard race to predict" because voters don't like either candidate. He said the results would hinge on whether Clinton could mobilize anti-Trump Republicans to show up at the polls and support her while getting a huge turnout in urban areas.

"I don't think there's any chance of Hillary Clinton winning Texas, but if she comes within single digits, that could be a big problem for Republicans in Harris County and the statehouse races here in Dallas County," he said.

Many down-ballot Republicans are worried that an anti-Trump crusade could affect their races.

Last week I told readers that Trump would win Texas but stumble just enough to hurt some Republican candidates on the rest of the ticket.

The CBS poll included 1,031 likely voters, questioned Thursday and Friday. It has an error margin of 4.4 percentage points, meaning results can vary by that much in either direction. You can check out how it was put together here.