Senate Minority Leader Mitch McConnell (R-Ky.) will file a brief in a Florida court in support of a lawsuit challenging the constitutionality of the new health-reform law.

The top Senate Republican will file an "amicus curiae" ("friend of the court") brief in the Florida case and has urged GOP colleagues in the Senate to sign onto the filing, too.

"While I strongly believe that we should repeal the law and replace it with the types of commonsense reforms Americans support, I also strongly support the efforts of over twenty States that have challenged this law in the courts," McConnell wrote in a dear colleague letter.

The effort is meant to build support by Senate Republicans for one of the highest-profile legal challenges to health reform, President Obama and congressional Democrats' signature legislative accomplishment in the past two years. It can be seen within the context of Republicans' vow to repeal the president's new health plan, a cornerstone of the case they made to voters in last week's election.

The suit challenges the constitutionality of a key part of the legislation, the so-called "individual mandate," or the requirement for all individuals to have health insurance. A judge ruled in October that the Florida suit, brought by 20 state attorneys general and the National Federation of Independent Business (NFIB), could proceed.

McConnell wrote that the healthcare law would "remove an important bulwark" against government intrusion.

"I hope you will join me in arguing to the court in the attached brief why that should not happen," the Republican leader wrote.

Senate leaders filing amicus briefs are not entirely without precedent. Senate Majority Leader Harry Reid (D-Nev.) filed one earlier this year in support of military families who were challenging a church's First Amendment right to protest soldiers' funerals.