The project is in its ninth year and is expected to cost at least $285 million. Suspending the work is part of the House Republicans' legislative agenda for this year.
Speaker Mike O'Neal said Republicans are committed to finishing the project but want to wait to see if construction and labor costs dip temporarily because of the recession.
But Senate Ways and Means Committee Chairman Jay Emler says that's not a good idea because resuming the work will cost even more money.
The Lindsborg Republican said it's a good idea to look at what's being done, but the project shouldn't stop.