In Texas, a proposal to use $181 million of the federal money to help build a toll road that will eventually form part of an outer ring around Houston has drawn criticism from some transportation advocates who warn that the project will spur more sprawl.

Two schools of thought are emerging as states decide what to do with their shares.

Kansas decided to concentrate its money on a few new projects that its transportation secretary, Deb Miller, called “game changers.” So it will spend nearly a quarter of its money building the next leg of a project to expand U.S. 69 in Overland Park, a bustling suburb of Kansas City. It will rebuild an interchange in Wichita in an area where developers want to put more retail space, rebuild a rural highway in Gove County that has heavy truck traffic, and complete a 10-year project to improve a corridor in McPherson County where work was stopped because the money had dried up.

“We wanted to build projects that would have a lasting impact, so that 20 years later people could look at them and see what we did,” said Ms. Miller, who added that the department was considering making plaques to show that the projects had been paid for by the American Recovery and Reinvestment Act of 2009, the official name of the stimulus law.

Others argue that the money should be used to fix the crumbling infrastructure that already exists. They note that for years, many states have put off much-needed maintenance to save money, and that repair projects can be done quickly. In the absence of a broader policy discussion about the future of transportation — which would involve wrestling with questions about sprawl and how to reduce dependence on foreign oil — these states have decided it is better to fix existing roads than to build new ones that would only attract more cars.

Maryland is taking the fix-it-first approach — and calls the $638 million it will receive in stimulus money most welcome, given that the state was forced to defer $2.1 billion worth of construction and repair projects when the economy soured. John D. Porcari, Maryland’s transportation secretary, said the state would quickly put some 10,000 people to work resurfacing dozens of roads, painting and repairing bridges and putting in guardrails.

“It’s like maintaining your car: if you neglect the relatively easy periodic maintenance, you’re building up to a very big bill — and eventually replacing it,” Mr. Porcari said. “Instead of having one or two or three megaprojects, we have literally dozens and dozens of projects in every corner of the state, which maximizes the ability of local firms to compete for them.”

Now contractors across the country — many of which have had to shed workers as construction slowed to a halt — are gearing up for more work. Jim Andoga, the president of Austin Bridge & Road, which does heavy highway work in Texas, said his firm had mothballed one of the asphalt plants it owned and let go about 50 workers. Other companies have had to lay off up to half of their workforce, Mr. Andoga said.