It's the responsibility of the local and state governments to pay to repair bridges on local streets or state roads. The federal government only pays to repair bridges on
USDOT FHwA Federal-aid Highways System.
Each program has a federal share and a state or local match. In the case of highway bridge replacement and/or rehabilitation, the federal share is 80%, which means that the local or state government has to come up with the other 20%. That 20% can be millions of dollars that local governments just don't have, and can't get.
Go to page 75 (76 counting the cover) of this PDF document for more detail.
There's more to repairing bridges and roads than just fussing at Congress to pass a funding bill.
As we all saw vividly with the Obama Administration's "Shovel Ready Projects" that shovel ready projects don't exist. The truth is, we do need to repair our bridges - desperately. But, it isn't as easy or simple as many people would have you think it could be. If it were that simple, the bridges would have been repaired decades ago. Yet, the problem is not going to get better, it's just going to get worse, and more expensive as time goes on.
If we're going to do this, we must have a system to manage the money, the contracting, and the auditing. FHwA doesn't have that in place at a level that could handle such a major undertaking. The only government agency that could potentially take on such a project would be the USACE (US Army Corps of Engineers). However, the Corps' overhead added to most projects they manage is 35%-40%. That means that for every Billion Dollars of work done, the Corps would spend $400 Million in General, Administrative, and Overhead costs alone.