Don't discount the fact that this is a 5 year program that the Senator has proposed. For the 36 million Americans unemployed [per the Bureau of Labor Statistics, U-6 unemployment rate of 11.3%)](http://www.bls.gov/opub/ted/2015/unemployment-rate-and-u-6-measure-in-january-2015.htm, I'd say they would take that work in a heart beat, whether you call it "full time" or not.
The Senator's program of $1 trillion substantially less than the $3.6 trillion that the American Society for Civil Engineers estimates would need to be spent by 2020, just to tread water at the bare minimum to get back to a functioning level. NOT as a infrastructure growth program. So really, the 5 year program will need to continue to be extended out for years. The time spent on engineered projects and the sheer quantity of projects that can be undertaken... there's plenty of work to justify.
I think you're underestimating all the types of jobs that are created just simply by investing in infrastructure. Engineers, inspectors, safety specialists, job training, supply chain of construction materials, supply chain of construction equipment and vehicles. And that's just construction. The Brookings Institute estimates that by infrastructure activity, only 15% of the jobs are technically Construction related, where 77% is Operations related.. These types of jobs have low barriers of entry in terms of formal education.
All the above being said, Standard & Poors has estimated that spending $1.3 billion in a year would create 29,000 jobs, add $2 billion to economic growth, and reduce the deficit by $200 million.. Take that same $1.3 billion a year of the Senator's program of $1 trillion over 5 years? Each year would have 5.8 million jobs created, $400 billion in economic growth and reduce the budget deficit by $40 billion a year.