General aviation pilot reported during taxi in an area with construction; a street sweeper crossed in front of them requiring evasive action to avoid a collision.

Narrative

My instructor did a long landing at ZZZ on runway XXC in an Extra 300L tailwheel. We got clearance from ground control to taxi back to parking on the Northwest side of the airport after we cleared the runway. The clearance was 'Taxi golf; cleared to cross runway XXL; 1; 2; to park.' They were doing construction at the end of runway XXL where we were crossing; so there were vehicles in the area that we briefed we needed to watch out for. In the Extra; you can't see very well in front of you since it's a tailwheel; so my instructor was doing S turns on the taxiway to be able to see. It's also a very high-performance airplane; and it tends to taxi faster than other airplanes. As we were approaching runway XXL; we were coming out of our S turn to the right when all of a sudden we noticed a street sweeper about 40' in front of us crossing right in front of our path going at a high rate of speed to avoid hitting us. As the student; I always keep an eye out for traffic; looking left and right before crossing runways; which I did today. I did not see the street sweeper crossing when we were approaching the runway; and neither did my instructor. My instructor had to stop decently fast to avoid a potential collision.What I think were contributing factors to this event were the fact that the construction crews did not judge how fast we were going; and thought they could travel in front of us in ample time. To give context; we were most likely traveling at about 20-25 kts across the ground. Another contributing factor is the reaction time to avoid conflicts in a tailwheel airplane; as you can't see half of the view in front of your path until you turn in the opposite direction. This doubles the reaction time to see and avoid conflicts compared to tricycle gear airplanes. The construction crew didn't notice this either; as they couldn't tell that we couldn't see in front of us.What I really think caused the event was the fact that my instructor and I could have slowed down through the construction area that we briefed about beforehand. But also the fact that the construction crews lacked situational awareness about aircraft operations; as they most likely didn't have radios. If they did have radios; then they might not know the aviation phraseology about taxi instructions.What I think can help solve issues like this in the future is having ATC ground control give aircraft a warning about construction vehicles in the area. But also having construction crews have radios where ground control can talk to them and give them warnings about traffic conflicts. Additionally; education to construction crews at airports about safe operation would be very beneficial in adding situation awareness to avoid conflicts. Finally; the education of controllers about the limited view of tailwheel airplanes would help as well. This would allow them to know that tailwheels need extra reaction time before they clear other traffic in front; whether that's an airplane or a ground vehicle.