The party has achieved some big goals this year, including laws to limit class-action suits.
The Bush plan would limit such suits to cases of gross negligence.
The decisions struck down measures to limit suits by people claiming injury, and the state's system of financing public schools.
Some conservatives say the trend toward limiting environmental suits is a needed correction after years of litigation that they describe as tantamount to blackmail.
But the Keidanren, Japan's powerful big business association, is currently lobbying to limit such suits once again.
The amendment expanded the sovereign immunity of states to limit suits against them by private individuals from other states.
Mr. Bush had wanted to limit suits to federal court, where damages are often lower than in state court.
Mr. Bush favors a measure that would cap settlements around the $750,000 level adopted in Texas and would limit suits to federal court.
But despite Wall Street's characterization of the measure as a modest change, its opponents say that it will significantly limit well-founded suits by investors.
The privilege can require courts to limit or dismiss suits that might disclose information harmful to national security.