It's up to the FCC to decide who wins the battle over "net neutrality."

On Monday, President Barack Obama asked the Federal Communications Commission to set the "strongest possible rules" to protect net neutrality as the agency writes new Internet access regulations.

The proposal pits liberal advocates of tougher regulation of Internet service providers—to treat them as public utilities—against conservatives who say it's an unnecessary government intrusion on the Web.

On Wednesday, Republican lawmakers railed against Obama's plan.

In a letter FCC Chairman Thomas Wheeler, they said proposals were "beyond the scope of the FCC's authority and would defy the plain reading of the statute.''

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In a tweet earlier this week, tea party favorite Sen. Ted Cruz, R-Texas, likened net neutrality to Obamacare for the Internet. "The Internet should not operate at the speed of government," he said.

Read MoreCruz compares net neutrality to Obamacare

The issue will be decided by Wheeler's five-member commission. Three of the commissioners, including Wheeler, are Democrats. the others are Republicans. The commission, which next meets in December, will not vote on the issue until next year, press secretary Kim Hart told the BBC.

Wheeler appears to want a more nuanced solution, according to The Washington Post. During a meeting Monday with officials of major Internet companies, Wheeler reportedly said: "What you want is what everyone wants: an open Internet that doesn't affect your business. ... What I've got to figure out is how to split the baby."

The president is asking for strict regulations that will ensure that all companies, big or small, get the same treatment from Internet service providers.

As of now, there's nothing to stop ISPs from granting so-called "fast lane connections" to whatever companies they want, including charging extra fees for such access.

"We cannot allow Internet service providers to restrict the best access or to pick winners and losers in the online marketplace for services and ideas," Obama wrote in his plan.

He's asking to end the process ISPs might use to slow down certain websites, which is often called "throttling" or "buffering." The preferential treatment called the "last mile" also could be affected. The last mile is the connection between consumers and ISPs.

Wheeler indicated that his approach would deliver some of what Obama wants but would also address the concerns of ISP companies such as Comcast, Verizon and AT&T that the regulations could stifle innovation and slow the growth of the country's broadband infrastructure.

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Tech giant Google, which has been a staunch supporter of net neutrality, has been quiet since Obama spoke but is part of the Internet Association, which issued a statement applauding Obama's move.

"The FCC must adopt strong, legally sustainable rules that prevent paid prioritization and protect an open Internet for users," it said. The trade group also represents tech companies, including Amazon, Netflix and Facebook.

Disclosure: Comcast is the owner of NBCUniversal, the parent company of CNBC and CNBC.com.