Donald Trump. Mike Segar/Reuters Donald Trump is losing support in the Republican stronghold of Texas.

The Republican presidential nominee's lead has fallen by so much that a poll released Thursday showed his Democratic counterpart, Hillary Clinton, within the margin of error, trailing Trump by just 4 points.

The poll, from the WFAA-TV and Texas TEGNA television stations, came after perhaps Trump's most damaging week of the campaign. It showed Trump up on Clinton by 47% to 43% in the Lone Star State, with a margin of error of 4 percentage points.

In the past two Texas polls posted to RealClearPolitics, Trump was found to be up 7 points in the Lone Star State.

"I think to put these numbers in context — it shows that Trump's position has eroded a little bit," said Matthew Wilson, an associate professor of political science at Southern Methodist University in Dallas.

He added: "His lead is down to 4 percentage points according to this poll, but even in the wake of some really terrible news for him, he still leads in Texas, which shows what a tough nut Texas is to crack for Democratic candidates right now."

Mitt Romney, the 2012 Republican presidential nominee, won Texas by 16 points; John McCain, the 2008 GOP nominee, carried it by 13 points; and George W. Bush carried his home state by 23 points in 2004 and by 22 points in 2000.

Texas has not turned blue since 1976.

The survey comes amid a tumultuous turn in the polls for Trump after the leaking last week of a 2005 video showing him making lewd comments about women and the emerging this week of several women who have accused him of sexual misconduct.

Business Insider's latest Electoral College projection shows Clinton on track to pick up 316 electoral votes, based on her polling leads in battleground states. The latest RealClearPolitics national polling average puts Clinton up by 5.3 points in a four-way race that includes Libertarian nominee Gary Johnson and Green Party nominee Jill Stein.