MIAMI (CBSMiami) – Florida Senator Marco Rubio has never backed down from a challenge, but his latest target is the President of the United States over an issue that could thrust Rubio further into the Republican spotlight.

Earlier this year, President Barack Obama’s administration issued new rules for insurance providers that mandated birth control coverage without co-pays. The administration issued some exceptions for the mandate including churches.

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However, church-run schools and universities, hospitals, and charities were not exempted from the new rule.

This has led to conservatives railing against the rule and saying President Obama’s administration is in a “war against religion.”

Senator Rubio jumped into the fight last week when he filed a bill that would repeal this part of President Barack Obama’s healthcare law.

“I don’t think the government should be forcing any institution to pay for something that institution finds to violate their conscience,” Senator Rubio told CBS4’s Tiffani Helberg.

“This is unprecedented because never before in the history of our country has the government tried to insinuate itself in the domain of one’s personal conscience,” said Archbishop Thomas Wenski.

The bill, which may not have much of a chance of passing in the Democratically controlled Senate, pits Rubio against Obama as election season heats up.

“Ultimately, the constitutional right of a religious organization not to be forced to violate their religious principals is of paramount importance in our country,” Rubio said. “It’s one of the founding principals of our nation.”

The White House said it gave religious institutions an extra year to comply with the rule and said individual churches that only serve a narrow population with similar beliefs can also seek exemptions, according to CBS4 news partner the Miami Herald.

“We are concerned that much of what is advertised as contraception is really chemical abortion,” Archbishop Wenski said.

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The White House also said 28 states already required insurers to cover the cost of contraceptives.

For Rubio, it’s a tough political issue that could endear him even more to the most socially conservative wings of the Republican Party.

His office is portraying the fight as one over freedom of religion rather than over women’s health.

The White House and Democrats are taking the exact opposite approach saying that there shouldn’t be discrimination between insurance companies that choose to cover drugs like Viagra with little to no co-pay, but then refuse to cover birth control.

Women CBS4 spoke to Monday seemed to side with President Obama in the very public fight.

“I think they should provide it and I mean, I’m Catholic myself, but I think that’s something wrong; it should be allowed by the Catholic Church,” said Lourdes Botioll.

“I think everybody has the right to make their own decision on what they want to do with their body and their reproductive organs,” said Daniela Montoya.

Gaby Moreno took it a step further.

“I think that it should be provided because men, for example, don’t have to deal with any of that and they don’t know what it’s like,” Moreno said. “It’s not fair that we have to pay all these things and always deal with these constant worries like birth control. We’re the ones that get pregnant and that’s kind of like a lot of men, unfortunately, are like, ‘Oh, it’s your issue.'”

It sets up an election year fight with Rubio possibly riding a wave of publicity and popularity to the presidential ticket as a vice-presidential candidate.

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Rubio initially said he wasn’t interested but may be softening his stance, recently saying he wants to do whatever he can to help the ticket.