Bernie Sanders said Sunday he thinks he can cut into his rival Hillary Clinton's lead among super delegates in the race for the Democratic nomination - a lead that allowed Clinton to salvage her substantial loss in New Hampshire's Democratic primary last week.

"If we continue to do well around the country and if super delegates - whose main interest in life is to make sure that we do not have a Republican in the White House - if they understand that I am the candidate and I believe that I am who is best suited to defeat the Republican nominee I think they will start coming over to us," the Vermont senator said Sunday on CBS' "Face the Nation."

He's already started the process of wooing those delegates: Sanders said he "just met with a couple last night."

Clinton entered New Hampshire's primary with the support of six of the state's eight superdelegates, party officials who can pledge to support any candidate they want. Of the state's 24 delegates awarded by the primary vote, Sanders won 15 while Clinton won nine delegates.

That means Sanders managed to tie but not beat Clinton in the total delegate count even though he beat Clinton in the popular vote by 22 percent. He would have to win the remaining two superdelegates to come away with an advantage heading into the Democratic convention.

Ray Buckley, the state's Democratic Party chairman and one of the remaining two New Hampshire super delegates is not allowed to support anyone in the primary and state Sen. Martha Fuller Clark said she might wait until after the primary is over to endorse a candidate, the Associated Press said.

In South Carolina, Sanders faces an uphill battle. Clinton leads him 59 percent to 49 percent in the latest CBS News Battleground Tracker. On "Face the Nation," Sanders says his campaign has closed the gap so he has the momentum, and predicted he would do "quite well" in both Nevada and South Carolina, the next two contests for Democrats.

Sanders said he has also started to close the gap in support among African American voters, but "we still have a long way" to go there. In South Carolina, 73 percent of black voters supported Clinton in the poll while just 26 percent supported Sanders.

He pointed to his surrogates, including former NAACP CEO Ben Jealous and Nina Turner, a black former state senator from Ohio and top Democratic Party official there. She switched her support from Clinton to Sanders in November.

"We have just great surrogates out there, we are going to be speaking in African American communities in the next week and I think you're going to see a lot of momentum for us," Sanders said.

The senator also predicted that his campaign will do very well in Minnesota and Colorado. He was interviewed from Denver, where he held a rally last night that he said drew 20,0000 people.

Sanders also weighed in on the death of Supreme Court Justice Antonin Scalia and Senate Majority Leader Mitch McConnell's declared intention to block President Obama from naming a successor

"It is beyond my comprehension and it just speaks to the unbelievable level and unprecedented level of Republican obstructionism against Obama from day one," Sanders said.

"The idea that the Republicans want to deny the president of the United States his basic constitutional right is beyond my comprehension," he added, pledging to "do everything I can" to try to get the Senate to consider and approve the nominee the president has pledged to put forward.

Asked what kind of levers the Democrats have to get the Republican-controlled Senate to consider the nomination, Sanders said they could rally the American people.

"There are very important cases that need to be heard that are not going to be determined if we do not have a ninth member of the Supreme Court," he said. "I think the issue is taking the situation to the American people, and I think fair-minded Americans no matter what their political point of view may be will say, 'this is absurd, this is obstructionism, this is not what democracy and the Congress is supposed to be about.'"

CBS News Political Reporter Rebecca Shabad contributed to this story.