The New York Times doesn't seem to use the term "vast" the way the rest of us would. It told readers that President Obama is:
"stymied by Republican lawmakers who refuse to go along with Mr. Obama’s call for vast new spending on the nation’s infrastructure."
The proposal in question would provide $300 billion in additional spending over the next four years. This is equal to roughly 0.4 percent of GDP over this period and less than 1.8 of projected federal spending.
Thanks to Robert Salzberg for calling this one to my attention.