Jeffrey D. Allred, Deseret News
FILE - Sen. Mike Lee, R-Utah, and Sen. Orrin Hatch, R-Utah, hug prior to speaking to Utah delegates in Akron, Ohio prior to the National Republican Convention on Monday, July 18, 2016. Lee is among a group in Congress arguing that a constitutional amendment setting term limits on lawmakers would help fix the federal government.

SALT LAKE CITY — Sen. Mike Lee is among a group in Congress arguing that a constitutional amendment setting term limits on lawmakers would help fix the federal government.

Lee signed on as a co-sponsor to a bill filed by Sen. Ted Cruz, R-Texas, and Rep. Ron DeSantis, R-Fla., that would allow House members to serve three two-year terms and senators to serve two six-year terms.

And Lee intends to unveil his own term limits legislation in the coming weeks. His version would limit members of Congress to 12 years in either house, Lee spokesman Conn Carroll said.

But the issue appears to have little support among congressional leaders.

Lee, who is starting his second six-year term, has been a proponent of term limits. He has said he would not impose one on himself without a law in place but would honor it if it were passed.

In a speech at the Heritage Foundation in November, Lee said voters shouldn't buy politicians' argument that their states would lose money, power and influence without representatives who have seniority and authority.

“It’s attaching a very high price tag to our most fundamental of rights, our right to vote,” Lee said, adding term limits is the best way to eliminate that argument.

Sen. Orrin Hatch, R-Utah, who is considering running for an eighth term, isn't jumping on the term limit bandwagon. He has built considerable power and influence during his 40 years in the Senate, where seniority is a factor in getting things done.

Hatch's office likes to point out that the senator passed 47 bills in the last Congress, 45 of which were signed into law — the most in the Senate over that two-year period.

As chairman of the Senate Finance Committee, Hatch is also poised to play a critical role in tax code reform and the effort to repeal the Affordable Care Act.

"The Constitution gives voters the power to term limit their representatives at each election, and Sen. Hatch trusts the judgment of American voters," said Hatch spokesman J.P. Freire. "Instead of engaging in the perennial Washington parlor game about term limit legislation that everyone knows is dead on arrival, the senator is focused on actually getting things done for Utahns like repealing and replacing Obamacare."

Calling it a "rare occasion," Utah Democratic Party Chairman Peter Corroon agreed with the Cruz and DeSantis term limits bill. He also used it to remind Hatch that Utahns support the idea.

"We thank him for his four decades of dedicated service and remind him that the people of Utah have specifically indicated their desire for him to not run for a record eighth term," Corroon said in a statement.

A survey conducted by Public Policy Polling last August found that 71 percent of likely Utah voters believe Hatch should not run again. A poll in October showed 88 percent of Utahns favor term limits for federal offices.

Cruz and DeSantis say their legislation is the first step toward reforming Washington.

"The American people resoundingly agreed on Election Day, and President-elect Donald Trump has committed to putting government back to work for the American people," Cruz said in a statement Tuesday. "It is well past time to put an end to the cronyism and deceit that has transformed Washington into a graveyard of good intentions.”

Trump backed term limits during his White House run, but the bill doesn't have much traction in Congress.

Neither House Speaker Paul Ryan, R-Wis., who has said he supports term limits, nor Senate Majority Leader Mitch McConnell, R-Ky., has indicated it could come up for a vote.

"I say we have term limits now. They’re called elections," McConnell said after the November election. "It will not be on the agenda in the Senate."