The U.S. political system is remarkably vulnerable to pressure from interest groups because power is so fragmented. We have three branches of government at the federal level, with a bicameral legislature, and 50 individual states, each with three branches of government and plethora of local governments. And you need them all on board to do anything big.
Imagine that you are the Sierra Club and you want to block construction of a new highway. You can lobby:
* The President, who signs the appropriations bill
* EPA, Department of Transportation, and any other three-letter federal agency that gets to weigh in on the project
* Congressmen and Senators of affected regions/states, and remember that Senators can filibuster legislation to make it require a super-majority
* State governors
* State legislators
* Local governments whose land the road will pass through
* Indian tribes, if their land is affected
And if above doesn't work, you can sue in federal/state court.
All that adds to the time and cost of a construction project, assuming that it will be even approved. And once its approved? You still have a million ways to delay/obstruct the project through lawsuits and lobbying the bureaucratic process.
That's why there are no 'shovel ready' projects. We'll never be able to build another Hoover Dam or the Interstate Highway system.
Obviously other countries have division of power too. But the effect is much less pronounced.
EDIT: As for why the U.S. of a century ago wasn't as paralyzed, well, that's partly because of the growth of the administrative state (bureaucracy), growing importance of interest groups as sources of campaign funds, more regulations in general (which makes lawsuits possible), and fragmentation of party discipline.