Incoming senators talk bipartisanship, but can they deliver?

Two newly elected senators, one from each party, pledged Sunday to work together in the new Congress, but it's clear that there are issues they are facing that could quickly put a damper on the spirit of bipartisanship.

Sens.-elect Thom Tillis of North Carolina and Gary Peters of Michigan appeared in a joint interview on "Face the Nation" Sunday, where both said Americans wanted to see Congress break the usual logjam.

"I think that the American people did not give Republicans a mandate, they gave us a chance," Tillis said, citing issues of manufacturing and job creation as opportunities for bipartisanship.

Peters, for his part, said the "clear message" of the 2014 midterm elections was Americans "wanting to see Washington work, having people come together and find that kind of middle ground to deal with the very tough problems that we're facing with the country."

Of course, lawmakers always find it easier to name issues where they could find agreement than to actually work together. And two looming issues, including two top cabinet posts that must be confirmed by the Senate as well as potential immigration reform legislation, could derail the best of intentions.

Does anyone want to be the next secretary of defense?

In the coming weeks, President Obama will seek confirmation of his attorney general nominee, Loretta Lynch, and will name his next choice for defense secretary, who will also need Senate approval.

"I hope that the president puts forth someone who will work for both sides. I think it's a great opportunity out of the gate to identify consensus nominees that we can all get around and support," Tillis said of the two positions. "Those are very important jobs. They need to be filled with someone who can take into account both sides of the equation, both ends of Pennsylvania Avenue."

Republicans have been noncommittal about Lynch's nomination, although some have indicated they will block any nominee who does not disavow the president's executive actions to shield millions of immigrants in the U.S. illegally from deportation.

Immigration is the other big issue that already has Democrats and Republicans sparring, and it was on display when Tillis and Peters weighed in.

"I'm afraid that the president's unilateral action is going to set us back," Tillis said. "Republicans and Democrats have both failed on this issue for decades and one of the reasons why is I don't think we've stabilized the problem by taking credible steps to seal the border. Then let's discuss what we do with the population who's illegally present."

But Peters said immigration is "a source of constant frustration to me" because he believes the House should have passed the Senate immigration bill, which has both Democratic and Republican support in the House as well as the backing of groups like the Chamber of Commerce.

"Congress needs to act," he said. "Instead of wringing their hands about the presidential action, Congress needs to pass a bill. We have a bill that's been on the table for a year and a half in the House. I believe that if the speaker would put it on the floor, it would actually pass...If my Republican friends want to work in a bipartisan way and find common ground, we're already almost there with a comprehensive immigration reform. All we have to do is pass it."

Other issues may have better luck getting through the new Republican-controlled Senate. Both Tillis and Peters said they would support a new authorization for the use of military force for the fight against the Islamic State of Iraq and Syria (ISIS).

"I think it is absolutely essential that we come together to show strength in the world community and we are stronger as a country when the president and Congress are united and I believe that we have to be a key player in that," Peters said.

Tillis said a new authorization "would probably be wise so that you move forward again...I think that would be a show of good faith from the president and i think it would give Congress more confidence that they're a part of the process."

  • Rebecca Kaplan

    Rebecca Kaplan is a political reporter for CBSNews.com.