Walsh's campaign has been silent about whether he plans to keep campaigning amid allegations that he plagiarized a research paper while studying for a master's degree at the U.S. Army War College in 2007.
Walsh has canceled campaign events scheduled for this week and spent Tuesday and Wednesday at his home in Helena. Tuesday was "a personal day" for him, spokeswoman Lauren Passalacqua said.
Campaign staffers have avoided questions about Walsh's plans for the race, and his normally active social-media sites haven't been updated for days.
Walsh has until Aug. 11 to drop out of the race against Republican Rep. Steve Daines, and the state's Democratic Party has until Aug. 20 to submit the name of a replacement candidate to the Montana Secretary of State.
"We are looking at our process" if Walsh decides to withdraw, party spokesman Bryan Watt said. Party leaders have not vetted any potential candidates, he added.
Watt said he did not know whether Walsh had made a decision and that the party stood behind the former lieutenant governor and former commander of the Montana National Guard.
According to party rules, the Democrats would hold a nominating convention to select a replacement. Convention delegates would include county party committee leaders, party executive board members and statewide and federally elected officials — about 175 people, Watt said.
They would gather to nominate potential replacements and hold rounds of balloting until one person received a majority of the votes.
Walsh has come under increasing pressure after The New York Times reported that he plagiarized portions of the 2007 research project he wrote while attending the U.S. Army War College in Pennsylvania. The editorial boards of Montana's three largest daily newspapers have called for him to withdraw his candidacy, while others have demanded that he apologize or forfeit his master's degree.
"Instead of closing ranks around Walsh, Democrats should call on him to do the right thing," The Billings Gazette wrote in a Sunday editorial. "Having repeatedly said that he wants to do the honorable thing, Walsh should stop campaigning and do his utmost to serve Montanans well in the remainder of his brief Senate appointment."
Walsh is running to keep the Senate seat he was appointed to by Gov. Steve Bullock in February when Max Baucus resigned to become ambassador to China.
Bullock communications director Dave Parker said Wednesday the governor has not spoken to Walsh since the Times' story was published.
Walsh previously said he made unintentional mistakes in not citing others' work in his paper on the spread of democracy in the Middle East. He also said he was being treated for symptoms of post-traumatic stress disorder at the time, but said he was not blaming PTSD for his mistake.
Associated Press writer Lisa Baumann contributed to this report.