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(CBS News) The Supreme Court this year has already handed down significant rulings affecting political speech, campaign finance and affirmative action, among other issues. With just about two weeks left to hand down the rest of this term's decisions, the high court has yet to address a series of other hot button issues, including the legality of an Obamacare rule, regulations covering abortion clinic protests, the president's power to make recess appointments, and the future of broadcast television.

The court will convene to issue its next rulings Thursday. Here's a look at some of the remaining cases still pending:

Obamacare's birth control mandate

The Supreme Court in March heard arguments in two cases -- Sebelius v. Hobby Lobby Stores, Inc. and Conestoga Wood Specialties Corp. v. Sebelius -- challenging an Obamacare mandate over birth control. The rule requires companies with more than 50 employees to provide comprehensive health coverage (including contraception) or pay a fine.

Not only are the cases politically potent -- hitting on divisive issues such as Obamacare, the left's "war on religion," the right's "war on women," and the notion of corporate personhood -- but they are also complicated, with potentially far-reaching implications.

"Hobby Lobby is a very significant case, almost any way the court could decide it," Steve Shapiro, the ACLU's national legal director, told CBS News.

A ruling in favor of Hobby Lobby or Conestoga would give for-profit companies unprecedented protections under the First Amendment. Based on the justice's questions during the oral arguments, the court may hand down a split decision.

To reach their ruling, the court will have to work through what Shapiro characterized as a "decision tree." First, the justices must answer whether a for-profit corporation can claim the First Amendment right of freedom to exercise religion. If so, the court must then determine whether Hobby Lobby has been "substantially burdened" by the contraception law. Even if the court decides both of those questions in Hobby Lobby's favor, it must then determine whether there is a "compelling government interest" to place that burden on corporations.

"Depending on where its off-ramp is, the case can have broader or narrower implications for other settings," Shapiro explained.

Abortion clinic buffer zones

McCullen v. Coakley presented the court with another question related to both reproductive rights issues and the First Amendment. The case is review a 2007 Massachusetts law that makes it a crime for speakers to be within 35 feet of any entrance, exit or driveway of an abortion clinic.

Shapiro said he'd be surprised if the court wrote a broad ruling against buffer zones all together, given how common they are. Every state has buffer zones around military cemeteries and funerals, for instance.

However, the petitioners in this case argue that the Massachusetts law is different, since it exempts clinic employees from the rule. Effectively, only those who oppose abortion rights are subject to the restriction, they argue.

Supreme Court skeptical of Mass. abortion buffer zones

During the January oral arguments, both the liberal and conservative justices expressed skepticism about the law, questioning whether there were less restrictive ways available to protect clinic patients.

Presidential recess appointments

The Supreme Court in the coming weeks will also issue a ruling in a case that could expand or limit the scope of presidential power. National Labor Relations Board v. Noel Canning calls into question President Obama's decision to appoint three officials to the National Labor Relations Board (NLRB) during a "pro forma" Senate session -- technically, the Senate was "in session," but in reality, no senators were at the Capitol to confirm the appointments.

Supreme Court skeptical of Obama recess appointments

The Constitution allows the president of the United States to make appointments when the Senate is in recess. However, Republicans in the Senate wanted to block the NLRB appointments, so they held "pro forma" sessions in order to make recess appointments impossible. The president simply decided that the "pro forma" sessions count as a recess.

Republicans have charged the president with overstepping the bounds of his powers -- and the Supreme Court in January seemed inclined to agree. Even liberal Justice Elena Kagan said that "congressional intransigence" may not be a good enough argument for the Obama administration's move.

Labor union rights

While the NLRB case addresses presidential powers, the Supreme Court has also taken up labor union rights in this term. In Harris v. Quinn, the court is considering whether Illinois home-care workers can refuse to pay "fair share" fees to a union for the cost of representation.

Currently, public sector unions must bargain on behalf of all workers, whether those workers have joined the union or not. The unions collect dues from members, but they are also allowed to collect "fair share" fees from non-union workers to compensate for the cost of negotiating on their behalf. The "fair share" fees cannot pay for any political activity. Revoking the right to collect "fair share" fees could be devastating for public unions -- workers could simply reap the benefits of the union system without contributing to it.

The petitioners in the Harris case are not technically public employees -- they are private home-care workers employed in a Medicaid-funded system.

Sarah Leberstein, a staff attorney for the National Employment Law Project, told CBS News that there are a range of potential outcomes in the Harris case. The court could uphold the current system, or it could issue a limited ruling that applies to the home-care worker system, or it could issue a broader ruling.

Yet even if the ruling applies just to the home-care worker system, it could have a large economic impact. There are currently an estimated 2 million home-care workers across the nation, Leberstein said, and a large number are funded through public dollars. That number will only grow as Medicaid expands under Obamacare. Projections put the home-care workforce at about 3 million in the next decade.

"What happens in this case or in upcoming years will have tremendous impact not only on this workforce, but on the jobs that are going to make up a huge part of the workforce in the future," Leberstein said, "and the services we're providing to baby boomers as they become more reliant on home-care services."

The future of broadcast television

In ABC v. Aereo, the Supreme Court is considering whether a new technology, one that relies on cloud computing to store programming, violates the Copyright Act. Parties on both sides are warning of the huge economic consequences that could come from the court's ruling.

Subscribers to the company Aereo can watch a program over the Internet -- or record a program to their remote DVR storage space and watch it later. Broadcast companies, including CBS, have balked at this technology, arguing that Aereo's service is more akin to a cable subscription than it is to a DVR service. By that logic, Aereo should have to pay the same fees that cable companies do to retransmit network shows.

By skirting retransmission fees, Aereo threatens to disrupt the way broadcast companies do business. The vast majority of TV consumers now get their programming from cable, satellite or fiber, making retransmission fees increasingly valuable.

However, others argue that if the court rules against Aereo, it could impact any number of businesses that rely on cloud computing -- services like Google Drive or DropBox that allow users to store their data on remote servers and access it on the Internet.

ABC v. Aereo: Will the Supreme Court change the way we watch TV?

"One thing that came through from the oral argument was the justices seemed quite aware of the fact that the case carries implications beyond the immediate context," David Sohn, general counsel for Center for Democracy and Technology (CDT), told CBS News. "I took that as encouraging, that they were thinking through the right questions about what the impact could be for technologies if they rule in a way that essentially offers a broad interpretation of the public performance right."

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