Updated

As polls began to close Tuesday night, the chairman of the National Republican Senatorial Committee brought a message straight to the man at the center of the midterm elections: President Obama.

"I think here's a chance not only for the nation to make a midcourse correction, but for President Obama, as well," Senator John Cornyn said. "If he'll work with us on those issues-like getting Americans back to work, cutting spending and debt, then I think he'll find a more-than-willing partner in the GOP."

However, the Texas senator also had a stern warning for the president from GOP incumbents.

"If he's going to continue to not listen to the American people and lecture them and tell them what he thinks is good for them despite their wishes, then I think we're in for a pretty tough period," Cornyn said. "And the electorate will cast their judgment for 2012."

"I think health care was, perhaps, the metaphor for what people find is so wrong with Washington these days," the senator continued. "Government doesn't listen, and it continues to spend money we don't have and borrow it from other programs like Medicare, which are already on a fiscally unsustainable path, and you get something that actually doesn't fix the problem, it makes it worse-higher premiums, higher taxes, and more raids on the Medicare trust fund."

Even with early Fox News exit polls revealing 73 percent of voters are angry or dissatisfied with the way government is working, Cornyn does not believe republicans will take the majority in the Senate. "I think that we will make substantial gains, but I think next cycle-in 2012 when there are only nine Republican seats up and 23 Democratic seats up-I think that's the year we turn the corner," he said.

Cornyn also addressed obstacles the GOP will face as the night unfolds, particularly, the Senate race in Washington state between incumbent Democrat Patty Murray and Tea Party favorite Dino Rossi. The state's vote-by-mail policy may keep the outcome of the election unknown for days.

The other challenge Cornyn sees that has been occurring all over the country is various kinds of voter fraud. "Ever since the [2008 Minnesota Senate] Coleman-Franken race, we decided that we would take it upon ourselves here at the NRSC to get prepared" for a protracted legal battle, Cornyn said. "We're working with the Republican Governors Association, which we can [ask] to help hire the lawyers and do the legal research and have all that ready to go."

"My hope is we won't need any of it because we'll win decisively in all these races," the senator continued. "But if we don't, then we'll have the information and the legal team ready to go to make sure that every vote is counted."