Sen. Ted Cruz (R-TX) on Tuesday argued that President Barack Obama and Democrats, not Republicans, were the ones trying to shut down the federal government because he insisted on funding a health care reform law that was passed in 2010.

Last week, Sen. Mike Lee (R-UT) called on Republicans to refuse to vote on a continuing resolution to fund the government if included any funding for Obamacare. Cruz said that the government should be shut down unless the Affordable Care Act was "fully" defunded.

"Under no circumstances will I support a continuing resolution that funds even one penny of Obamacare," Cruz told The Heritage Foundation on Tuesday. "In order to win this fight, we need to get 41 Republicans in the Senate to make the same commitment or we need 218 Republicans in the House."

"The next step will be that President Obama and [Senate Majority Leader] Harry Reid will scream and yell, 'Why are those mean and nasty Republicans threatening to shut down the government over Obamacare?'" he continued. "And at that point, we've actually got to stand up and fight."

"We've got to stand up and make the argument and win the argument that, 'No, that's not true. We have voted to fund the federal government. We want to fund the federal government. Why is President Obama threatening to shut down the federal government? Because he wants force Obamacare down people's throats.'"

One reporter pointed out to Cruz that polls showed that most people thought that defunding a law and shutting down the government was not the proper way to govern.

The Texas senator, however, argued that some polls had been crafted as tools of advocacy.

"Even phrased in the most ridiculous, offensive way, half of Republicans said, absolutely," he noted. "Now, what's interesting is if you frame it the other way, 'Should President Obama shut down the federal government in order to force Obamacare on individual families even though corporations are getting a waiver?' You know what? Those polls numbers flip around immediately."

"It is the only strategy that I'm aware of that can work," Cruz explained. "And if we do not pursue this strategy, we are saying, we surrender. Obamacare will remain a permanent feature of the American economy. And you know what? There are an awful lot of members of Congress in both Houses who campaigned explicitly on saying, we will fight to repeal Obamacare."

Update (1:45 p.m. ET): Cruz later argued that a government shutdown would not be a "horrible calamity" because the same thing essentially happened every weekend.

He pointed to the government shutdown of 1995 as example: "Number one, the world didn't end. Planes didn't fall out of the sky, Social Security checks didn't stop, military paychecks didn't stop, we didn't default on our national debt. What happened was that non-essential government services were temporarily suspended while the [continuing resolution] expired. Now, that happens every single week on the weekend. On Saturdays and Sundays, we see temporary partial government shutdowns and the world doesn't end."

Watch this video from The Heritage Foundation, broadcast July 30, 2013.