Updated: 10:22 a.m.

National Republican Senatorial Committee Chairman John Cornyn (Texas) predicted a “good day” for his party on Nov. 2 and estimated Sunday that there are 11 or 12 Senate races in “very close contests.”

Democratic Senatorial Campaign Committee Chairman Bob Menendez (N.J.), meanwhile, pushed back against the possibility of a GOP majority in the Senate in the next Congress.

“None of our Republican incumbents are in any trouble,” Cornyn said on CNN’s “State of the Union.” “The only question is how many seats we’re going to pick up. I think we’re going to have a good day on Nov. 2. I don’t know how high or how wide that tsunami will be, but it will be significant.”

Menendez acknowledged that Democrats are likely to lose some seats in the midterm Congressional elections, but he shot down the possibility that the GOP could pick up the 10 seats it needs to secure the majority.

“The difference between a tsunami and losing some seats is the suggestion that they can take over the majority. That will not happen,” he said during the joint interview on “State of the Union.”

He also argued that a “triple crown” victory for Republicans — pickups of President Barack Obama’s former seat in Illinois and Vice President Joseph Biden’s former seat in Delaware and an ousting of Senate Majority Leader Harry Reid in Nevada — won’t happen.

“They’re not going to win any of that triple crown,” Menendez said. “We will be in the majority in the United States Senate on Nov. 3.”

Menendez also answered questions about his decision to introduce an immigration overhaul proposal last week, just before the Senate adjourned for the campaigns.

The bill was a follow-up to his pledge last month to introduce legislation before the year’s end, and he said Sunday that it would serve as a starting point for legislators in the next Congress, or possibly in November during the lame-duck session.

“What I introduced had a series of Republican initiatives in it as an invitation to bring my Republican colleagues to the discussion and engage them on the critical issue of a country both in its national security, its national economy and how we deal with people in this country who are undocumented,” he said.

Cornyn used the question to hammer at Democrats for not taking up an extension of the 2001 and 2003 tax cuts before adjourning. The Bush-era tax cuts expire Jan. 1, and Obama and Democratic leaders favor extending the cuts only for the first $250,000 in income for couples ($200,000 for individuals). Republicans and some Democrats want the tax cuts extended across the board.

Cornyn was asked about his recent appearance at an event held by the Log Cabin Republicans, a gay rights group, and whether his party needs to be more welcoming to the gay and lesbian community. He responded by emphasizing his socially conservative bona fides.

“I’m a social and fiscal conservative, and my record on pro-family provisions or issues is very clear,” he said. “But I felt it was important to reach out to those who want to try to deal with this runaway administration and majority when it comes to spending and debt and high joblessness. That’s something we can agree on.”