Chu spoke about the project in response to a question during an appearance at the Detroit Economic Club.
Michigan State won a national competition to land the project in December 2008, and work is under way to design the Facility for Rare Isotope Beams.
The facility is designed to accelerate atomic nuclei to high speeds, then shatter them to create rare isotopes not found on Earth.
Chu and others from the Obama administration are constrained about discussing funding decisions until after budget officials release the president's fiscal year 2013 spending proposal in early February.
"I am trying to be as neutral as possible on the project. No decisions have been made," Chu told reporters in Detroit. "We have to be very careful because we can't be starting six things, and we can only afford four things or five things."
U.S. Sen. Carl Levin, D-Mich., responded with a statement sharply critical of any move to back away from the Michigan State project.
"The Department of Energy entered into an agreement with MSU that includes time schedules and funding commitments by both parties to bring FRIB into operation by 2018, Levin said. "MSU and the state of Michigan have met their commitments in this partnership, and it would be unconscionable if the federal government failed to live up to its commitments in meeting this critical national priority."
U.S. Sen. Debbie Stabenow, D-Mich., said a withdrawal of U.S. backing at this stage "would be absolutely unacceptable."
A Michigan State spokesman said university officials remain confident the research effort will continue. He said he bases that on repeated positive signs from the Energy Department staff and bipartisan expressions of support from Congress as recently as December.
"Everything that MSU has done so far ... indicates to us that the project is on track and ready to go," said Kent Cassella.
Energy Department spokesman Damien LaVera said Wednesday evening that Chu was not trying to stake out any change in the department's views on the physics research facility.
"While the department continues to believe this is an important project, our nation faces tough economic times and difficult budget choices have to be made," LaVera said. "At this point, we have not made a decision on the level of support for this project in (fiscal year) 2013."
In August, Michigan State officials said they expected to start construction on the Facility for Rare Isotope Beams in summer 2012. So far, the university has hired about 100 engineers and others, and construction itself will employ about 5,000 people full-time, Cassella said.
Once completed, the facility will draw researchers in a range of scientific fields from around the country, he said.