President Donald Trump made a "very risky proposition" when he said the United States will build the wall along the Mexican border even if it means a government shutdown, Sara Fagen, a former senior aide to President George W. Bush told CNBC on Wednesday.
Trump made the comments during a rally in Arizona on Tuesday. If Congress does not reach a funding deal that the president signs into law by a Sept. 30 deadline, the government will shut down.
Fagen, who served as White House political director for Bush, said Republicans were blamed for shutting down the government in the past and it didn't "end well for the party." If it happens this time, the GOP will be blamed again since the party has control of Congress and the White House, she noted.
"Trump is going to have to eat his words on this," she said in an interview with "Power Lunch."
"Politically, it would be far worse to shut the government down and people not get their Social Security checks than to fail to erect the border [wall] that most of the country doesn't want."
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.
Fagen also reiterated her belief that the "dumbest thing" Trump has done while in office is picking a fight with Senate Majority Leader Mitch McConnell, who is the most important person in getting Trump's legislative agenda accomplished.
That said, McConnell has a "very thick skin," she said.
"He wants positive accomplishments to run on in 2018. And he's a big boy and I suspect he'll let it roll off his back."
McConnell released a statement on Wednesday that said, "The President and I, and our teams, have been and continue to be in regular contact about our shared goals."
He went on to say, "we are committed to advancing our shared agenda together and anyone who suggests otherwise is clearly not part of the conversation."
The White House did not respond to a request for comment.
— CNBC's Jacob Pramuk contributed to this report.