National Republican Senatorial Committee Chairman John CornynJohn CornynWhite House officials expect short-term funding bill to avert shutdown Spending bill delay raises risk of partial government shutdown support GOP leaders to Trump: Leave Mueller alone MORE (R-Texas) conceded Sunday that it will take two election cycles for his party to take control of the Senate.

Only two days shy of the midterm elections on Tuesday, Cornyn said Republicans will "make a lot of headway" but "I'm not predicting that we will get the majority this cycle."

"I think it probably is going to take two cycles, but there is certainly a potential there, depending on just how high and how broad this wave election is," Cornyn said Sunday on ABC's "This Week."

He pushed back on reports that Republicans were pulling their support for Senate candidate Joe Miller, who is in a close race with incumbent Sen. Lisa MurkowskiLisa Ann MurkowskiProposed budget for Indian Health Services won't treat Native American patients equally Keep anti-environment riders for Alaska out of spending bill Industry should comply with the Methane Waste Prevention Rule MORE (R-Alaska), running as a write-in after he defeated her in the Republican primary, and Democratic candidate Scott McAdams.

"Well, that's not the case," Cornyn said. "We are supporting the nominee of our party, which is Mr. Miller, but we are concerned."

With the tight race, Cornyn said that what Republicans "want to make sure of is that the Democrat doesn't win."

Although Democrats aren't pouring money into the Alaska campaign, Democratic Senatorial Campaign Committee Chairman Sen. Robert MenendezRobert (Bob) MenendezPoll: Menendez has 17-point lead over GOP challenger Russian attacks on America require bipartisan response from Congress Justice Dept intends to re-try Menendez in corruption case MORE (D-N.J.) said "we believe that Scott McAdams actually has a real chance of winning this race," saying Miller has lost his footing.

"I think he has a real opportunity here," he said.

There was still plenty of disagreement on whether Democrats and Republicans will take a path of cooperation or one of gridlock heading into the next Congress.

Menendez argued that Republicans have been asked to come to the table with their ideas while Cornyn countered that his party hasn't been allowed to contribute.

"President Obama himself said Republicans have come along for the ride, but they have to sit in the back of the bus," Cornyn said. "But really what we need to be focusing on are jobs, spending and debt. That's what's created this coalition of support, disaffected Democrats, independents and Republicans that are going to sweep many Republicans into office on November 2nd."

Menendez countered that Republicans took a stance against the Obama administration before any proposals were sent to Capitol Hill.

"We reached out to Republicans from the very beginning," he said. "It's not about being at the back of the bus. But when President Obama came to Capitol Hill when we were trying to get this economy moving on the Recovery Act, before he got to the Capitol, Republican leaders were saying dead on arrival, before he even got to engage them."

The agenda shouldn't be about making Obama a one-term president but "I thought it was about creating jobs and growing the economy," he said.

Any Republican gains on Tuesday should give the GOP a chance to generate an agenda on jobs and deficits.

"The administration and Democrats, who have been in charge now in the House and Senate for four years and in the White House for two years, don't want to seem to accept any responsibility," Cornyn said. "I think that's what this election is about, is assigning responsibility, and giving Republicans a chance now to deal with the matters that concern them most."