Barra began facing that ire on Wednesday during two days of meetings this week with lawmakers from states hit by the automaker's plans to shed as many as 15,000 jobs and cancel production at five plants in North America.
Labor leaders worry that GM will ship the jobs overseas.
Since early 2017, GM has cut two of the three production shifts at the OH plant that makes the Chevrolet Cruze vehicle, eliminating 3,000 jobs.
Autotrader analyst Michelle Krebs said the world has changed dramatically since the bankruptcy and to have a healthy company, Barra needs to make tough decisions.
Sherrod Brown, Ohio's other senator and a Democrat, said Barra will speak with the union about accelerating decisions on where the company locates plants.
The automaker has said the factories aren't running at full capacity and are building mostly slow-selling and less-profitable cars. Barra added that GM workers may have an opportunity to find employment at the many growing GM factories around the country.
"These plants are unallocated right now.I have a responsibility to work with the UAW on that" Barra explained.
GM had conversations with the union past year about making concessions that would give the plant a better chance to stay open, said two people familiar with the matter.
Portman said he and Brown urged Barra to speed up talks.
"We are bringing new technology that engineering work has developed", she said. Gary Peters, among other lawmakers, on Thursday.
"I share their concerns about the impact the actions we announced last week will have on our employees, their families and the communities", Barra said in the statement. "These were very hard decisions - decisions I take very personally".
In another tweet, the president raised the prospect of additional tariffs on auto imports, saying "G.M. would not be closing their plants in Ohio, Michigan & Maryland" if traditional passenger cars were subject to a 25 percent import tax.
"I'm hopeful that we will get a new product here", Green said in a telephone interview. "We have a lot going for us here".
Barra arrived in Washington for meetings with angry lawmakers, including Senate Democratic leader Chuck Schumer, and members of Congress from OH and Maryland on Wednesday. A transmission and electric motor plant outside Baltimore was among the facilities slated for closure next year. "We are trying to do the right thing because we think OH is a very important auto state".
The announcement came as the United Auto Workers union on Monday sent a letter to GM formally objecting to the decision to end production in 2019 at four USA plants, saying it violates commitments made during contract talks in 2015. She was also expected to meet with lawmakers from MI on Thursday, among other meetings.