Charles Ommanney | Getty Images
A U.S. border patrol agent on the U.S. and Mexico border near Sunland Park, New Mexico.
During the campaign, Trump promised to build a wall along the entire U.S.-Mexico border to help crack down on illegal immigration. While he said Mexico would fund the project, Mexico has dismissed the idea.
The White House has sought federal funding for the structure, but Democrats have pledged not to back that spending in a bill. The GOP will need Democrats’ votes to keep the government open.
On Wednesday, House Speaker Paul Ryan said he doesn’t think a government shutdown is necessary and pointed out that most people don’t want it to happen.
However, Ryan also said he and the president “completely agree” on the need for a border wall.
Fagen said there may be a middle ground if Trump and party leaders can come up with a compromise, such as money for pieces of a wall.
However, she stressed that the most important thing Republicans need to focus on is tax reform, which she called a “win, win, win for everyone.”
“If the government gets shut down or we get into this multiweek/month fight over this border wall it’s just another distraction over what is a meaningful agenda item that could help all their political prospects,” said Fagen, a CNBC contributor.