WASHINGTON (Reuters) - A White House adviser on Sunday said he was optimistic Congress will approve at least part of President Barack Obama's proposals to reduce gun violence in the wake of December's massacre at a Connecticut elementary school.

Just hours before Obama was to be sworn in for his second term in office, White House adviser David Plouffe said on Sunday talk shows he felt there was support in Congress for some measures, including universal background checks for gun buyers and limits on high-capacity clips.

"I'm confident some of the measures you mentioned - clips, universal background checks - I think there are 60 votes in the Senate and 218 in the House, that the president would sign," Plouffe said on ABC's "This Week," citing the vote threshold to pass legislation in the two chambers.

"We don't expect it all to pass, or in its current form, but we think there's elements of this that are absolutely critical," Plouffe said.

Obama last week proposed the biggest U.S. gun-control push in decades, including a ban on military-type assault weapons and mandatory background checks for all gun buyers to prevent mass shootings like December's Newtown, Connecticut, school massacre in which a gunman killed 20 children and six adults.

Gun advocates led by the powerful National Rifle Association have mobilized to fight Obama's plan. With gun ownership rights enshrined in the Second Amendment of the U.S. Constitution, gun restrictions have long been a divisive issue.

Republicans on Sunday said Obama's key proposals had little chance in Congress, and said Obama's policies would not have prevented the Newtown shooting.

Reinstating the ban on assault weapons that expired in 2004 is widely seen as having little chance in Congress.

"Let's do things that will make a difference here, rather than take one more opportunity to go at an old agenda," Missouri Senator Roy Blunt said on "Fox News Sunday".

"We had bans on things for a decade. That didn't seem to make any difference at all, but, during that same decade, our willingness to share information about mental problems, our willingness to share information between security officials and police officials, all declined," Blunt said.

Wyoming Republican Senator John Barrasso said Obama "ignored the major issues of mental health and violence in society in the media and video games, and he has focused so much on what may be happening at gun shows or on gun shelves at gun stores that I think he is failing to try to really find a solution to the problem of the tragedy of Newtown."

Barrasso, speaking on CNN's "State of the Union," also noted Senate Majority Leader Harry Reid, a Nevada Democrat, had voiced doubt about prospects for reinstating a ban on assault weapons.

"I don't think Senator Harry Reid even brings it to the Senate floor because he has six Democrats up for election in two years in states where the president received fewer than 42 percent of the votes," Barrasso said.

"And he doesn't want his Democrats to have to choose between their own constituents and the president's positions," he said, highlighting the political perils of gun control legislation for Democrats from pro-gun western and rural states.

(Reporting by Vicki Allen; Additional reporting by Thomas Ferraro and Leslie Wroughton; Editing by Sandra Maler)