There are two national firms that stand out for being focused on handling major plaintiff-side appeals and constitutional issues. Both are based in DC but handle cases all over the country--in the U.S. Supreme Court and the lower courts:
1.) Gupta Wessler PLLC, Washington, DC - (
http://www.guptawessler.com). "Gupta Wessler PLLC aims to be the nation’s premier private appellate boutique for plaintiffs and public-interest clients. We handle high-stakes cases in the U.S. Supreme Court and courts across the country, approaching each matter with a fresh perspective, a bird’s-eye view of the law, and a creative and strategic sense of how to frame the issues for success."
2.) Center for Constitutional Litigation, Washington, DC - (
http://www.cclfirm.com) "An appellate firm for the plaintiffs’ bar since 2001, the Center for Constitutional Litigation, P.C. has represented parties in numerous high-profile cases in the Supreme Court of the United States and federal and state appellate courts. Trial lawyers from across the country turn to CCL to represent their clients in civil appeals involving complex legal issues, and also to assist at the trial level."
Gupta Wessler is the younger, more dynamic firm, and is doing work on an incredibly wide range of issues (class actions, arbitration, and consumer law to environmental justice, civil rights, and gun control) for both big and small plaintiffs' firms and non-profits. The lawyers have blend of top appellate and public interest credentials.
Center for Constitutional Litigation is older and smaller (just four lawyers) and is more focused on issues like constitutional challenges to damages caps. They seem to have an affiliation with the American Association for Justice, which is the national trial lawyers' organization.
Gupta Wessler has a summer associate program and a post-grad fellowship program:
http://guptawessler.com/recruiting/
CCL's website doesn't say if they take summers or what their hiring policies are.