In a letter to Attorney General Catherine Cortez Masto, Heller echoed concerns that the bill will create unfunded mandates and questioned the constitutionality of requiring everyone to obtain health insurance.
"A law is not simply justified by its intentions. Congress must honor states' rights and the equality of each citizen," Heller wrote.
Immediately after the president signed the bill Tuesday, attorneys general of at least 13 states filed suit to block its implementation.
Gibbons on Monday renewed his call for Masto, who is a Democrat, to sue the federal government, and said his administration would act on its own if she declines.
Masto said her office is conducting a legal analysis of the law. "It is one thing to simply say, 'let's sue'; it is another thing to have a legal basis to support such litigation," she said.
She said her office also was waiting to see the outcome in the Senate of a health reform reconciliation bill before deciding how to proceed.
Also on Tuesday, Republican U.S. Senate candidate Danny Tarkanian announced he was forming a committee to spearhead a ballot initiative for a state constitutional amendment guaranteeing health care freedom. He said he would launch the effort Wednesday in Las Vegas, and hopes to collect more than 100,000 signatures by a June deadline to qualify for the November ballot.
Tarkanian is one of 12 Republicans hoping to win the GOP nomination in June and challenge Democratic Sen. Harry Reid — a main architect of the health reform bill — in the fall.