Current polls put both Joe Biden and Bernie Sanders, the two leading Democrat contenders, slightly ahead of Mr Trump.
In the last two weeks four Republican members of Congress announced they will not seek re-election in 2020, when congressional elections happen on the same day as the presidential vote.
That brought the total stepping down to 11, a third of the entire Texas congressional delegation. Further announcements are expected.
Those standing down include Will Hurd, 41, the only black Republican congressman in America. He faced losing his district, which has a majority Hispanic population.
The latest congressman to stand down was Kenny Marchant, whose precipitous decline in the Dallas suburbs has alarmed Republican strategists.
In 2014 he won by 33 points, but that was down to just three points in the 2018 midterm elections. In presidential votes the district voted for Mitt Romney by 22 points in 2012, but for Mr Trump by only six points in 2016.
The Democratic Congressional Campaign Committee has ramped up its efforts, establishing offices in Texas, gleefully mocking the “Texodus,” and vowing to submit Republicans to a “long and expensive 15 months.”
Zac McCrary, a Democratic pollster, said: “Trump has really turned out to be an accelerant for energising young voters, and voters of colour. At the same time Trump has so deeply alienated suburban white voters in numbers that are mind-boggling.”