During a town hall meeting in Spanish Fork, Utah, Lee criticized the "blatant" and "unfair" characterization of his proposal as a shutdown threat.
"What I'm trying to do is avoid a shutdown," he countered, explaining the healthcare law was "unaffordable" and "fundamentally unfair."
Many Republican lawmakers in both chambers are advocating a move to block any funding measure that includes ACA funding. But some Republican lawmakers and strategists have expressed concern such a stance could lead to a government shutdown -- and voters will hold the GOP responsible when they go to the polls.
Most House and Senate Republican leaders have declined to sign on to the defunding strategy.
Heritage Foundation President James DeMint, a former U.S. senator from South Carolina, has urged voters to replace any GOP congressional member unwilling to vote to defund the healthcare law during September's budget showdown.
DeMint dismissed fears Republicans would catch voter ire for a shutdown.
"The risk of that is so much less than the risk to our country if we implement Obamacare, and so I'm not as interested in the political futures of folks who think they might lose a showdown with the president," DeMint said Monday during town hall hosted by Heritage Action, the foundation's political arm, in Fayetteville, Ark.
Two other senators said they won't support measures to fund government if it includes funding for Obamacare -- Sens. Ted Cruz of Texas and Marco Rubio of Florida, both considered potential GOP presidential candidates in 2016, CNN said.
Cruz, speaking at the news conference last week, said Republicans have the most leverage now as they try to get rid of the healthcare law.
"I believe that now is the best time we have to defund Obamacare," he said. "It's clear the wheels are coming off."
The continuing resolution that keeps the government running expires Sept. 30, also the end of the fiscal year.
Cruz: Welcome to politics' 'silly season'
Conservative Sen. Ted Cruz, R-Texas, says the national spotlight on his citizenship only demonstrates that political "silly season" is in full swing.
Cruz told CNN recently he didn't mind answering the questions about where he was born and where he's a citizen, but any question about whether he's eligible to be president are best left to the legal experts.
Cruz's citizenship became public fodder when it was revealed he was born in Canada to an American mother and Cuban father, giving him dual citizenship for the United States and Canada.
"If you don't have anything to hide, there's no big deal," Cruz said.
His mother was born in Wilmington, Del., "so under U.S. law, I'm an American citizen," he told CNN, explaining that he moved to Texas when he was 4 years old and lived in Houston for most of his childhood.
"It's always been my home," he said. "And when I was a kid, my mom always told me that if I wanted to, I could affirmatively choose to claim Canadian citizenship. But I got a U.S. passport when I was in high school, I never did anything to claim citizenship, and I thought that was the end of the matter."
Turns out, it wasn't the end of the matter.
After The Dallas Morning News reported about his dual citizenship, Cruz said he was ending any Canadian citizenship he may hold. But renunciation of his Canadian citizenship comes at a cost -- a four-page application and a $100 fee.
"Serving as a U.S. senator, I was an American by birth, and serving as a U.S. senator, I think it's appropriate I be only an American," he said.
Cruz's renunciation of his Canadian citizenship has fomented speculation that he's mulling a run to be the GOP presidential nominee in 2016 -- and with the abundance of social media, his citizenship issue could rear its head again ... and again ... and again before Election Day rolls around.
Just ask President Obama. Birthers have been dogging him since before the 2008 presidential election, charging that he wasn't born in the United States. Even after he produced a long-form birth certificate, the challenges remain.
Senate candidate Liz Cheney fined for lying about residency when buying fishing license
There's a bit of irony about getting caught lying to obtain a fishing license.
Still, it's a finable offense: Just ask Liz Cheney, daughter of former Vice President Dick Cheney and U.S. senatorial candidate in Wyoming.
Cheney had to pay a $220 fine for lying about her residency when applying for a fishing license, the Jackson Hole (Wyo.) News and Guide reported.
Candidate Cheney "fail[ed] to meet residency requirements as required," the ticket signed by Wyoming Game and Fish Jackson Supervisor Tim Fuchs said.
Wyoming resident fishing and game licenses require purchasers to sign a residency statement, swearing they have lived in Wyoming for at least a year and "have not claimed residence anywhere for any purpose during the one year immediately preceding the purchase of this license."
Cheney has said she bought the license in 2012 after buying a house near Wilson earlier in the year, the newspaper said. She moved to Wilson from Virginia.
A resident license costs $24 and a non-resident one costs $92.
She said that she did not know she was required to live in Wyoming for the immediately previous 365 days to qualify as a resident, the News and Guide said. She said she never told the clerk who sold the license that she had lived in the state for a decade, even though the clerk wrote "10" under the years-of-residency section.
The News and Guide said $220 ticket included a $180 fine plus court fees and costs.
La. Gov. Jindal ranks last among GOP governors, poll indicates
Louisiana Gov. Bobby Jindal has lowest approval rating among Republican governors, a recent Public Policy Polling survey indicated.
Jindal's approval rating among state voters fell to 28 percent, while 59 percent of respondents said they disapproved of the job he's doing, results of the Democrat-affiliated polling agency indicated.
The results mean Jindal not only is the most unpopular Republican governor of any state but also the second most unpopular governor overall, the Raleigh, N.C., polling agency said.
Jindal, barred from seeking another gubernatorial term because of term limits, has been preparing for a possible 2016 presidential bid. However, PPP said its poll indicated only 17 percent of Louisianans said they thought he should seek the presidency, while 72 percent held the opposite view.
Three years ago when the BP oil disaster in the Gulf of Mexico was making headlines, PPP found Jindal to be the most popular governor in the country with 58 percent of voters approving of him and 34 percent saying they disapproved.
Results are based on phone interviews with 721 registered voters conducted Aug. 16-19. The margin of error is 3.7 percentage points.