OK, so take a deep breath, slowly exhale, and sincerely and non-confrontationally ask why. Why exactly do they feel they can't they commit to any dates? Is the scope too undefined to estimate? Do they lack experience and fear their estimates might get them committed to an impossible schedule? Both problems can be addressed with
attention to the basics of a good step-by-step planning process.
To address that fear of being wrong, you can coach them through development of their estimates. Walk the individual through the process of decomposing their work into tasks they do feel comfortable estimating. They may need to just define tasks more explicitly to make clear what their work is. Or they may need to break certain activities down into a series of shorter tasks. Get support from a more experienced functional peer to help develop the estimate.
Ask what work they don't know enough about yet, and help them define concrete steps they can take to clarify the unknown. (Those pieces can get a rough schedule estimate now, and you can refine the estimate later when more is known.) You can indicate in the project plan that there's schedule risk for now in those areas, and closely monitor progress until you and the team member feel more confident in the effort and estimate.
Perhaps the root problem is risk. Refusal to provide schedule estimates when the risk is high is not uncommon. At least in this case the lack of commitment has brought another risk area to your attention early. To reduce the level of risk to get an estimate, start just as above with decomposing the effort into smaller tasks. Work together to define what can be done based on what is known and what can be done to convert the unknown into the known. Those tasks can be estimated and incremental milestones can be established to re-review the risk. For the balance of the work, you may have to agree to put a broad placeholder into your schedule to be refined at a each interim milestone. Be sure to integrate what you have learned into your risk assessment and mitigation plan.
You may also be hitting an extreme set of unknowns that point to the need for project-wide iterative planning. See Spiral/Iterative Project Phase Approach for guidelines on how to plan projects in sections and concentrate on getting commitments to the immediate next set of work.
You might want to read the information in Pete's Estimating Laws. This tongue-in-cheek list provides some "universal laws" that provide the project manager with amusing insights into possible sources of estimating error. "Dispelling Fear: Something to Get Exorcised About" covers the benefits of getting others to explicitly and openly discuss risks and a process for "unblocking" team members so they can move forward.