"My legislation will ensure that patients are not overburdened and that the administration will keep their commitment to the American people, or we get back to work on a better solution," Roberts said in a statement.
The exchanges are the centerpiece of healthcare reform, offering a venue for the uninsured to purchase coverage using subsidies from the government.
Enrollment is scheduled to begin on Oct. 1, with coverage starting Jan. 1 of next year.
Federal health officials say they are on target, and blame Republican opposition to ObamaCare for any delays.
Roberts's bill is co-sponsored by Sens. James InhofeJames InhofeTaiwan deserves to participate in United Nations Optimism rising for infrastructure deal Repeal of Obama drilling rule stalls in the Senate MORE (R-Okla.), John BarrassoJohn BarrassoPoll: Sanders most popular senator in the US The animal advocate Trump climate move risks unraveling Paris commitments MORE (R-Wyo.) and Thad CochranThad CochranPicking 2018 candidates pits McConnell vs. GOP groups Overnight Defense: FBI chief confirms Trump campaign, Russia probe | Senators push for Afghan visas | Problems persist at veterans' suicide hotline Senators ask to include visas for Afghans in spending bill MORE (R-Miss.).