Republicans are "within striking distance" of sweeping the Senate races they need to win the majority, Sen. John Cornyn (R-Texas) claimed Thursday.

Cornyn, the chairman of the National Republican Senatorial Committee (NRSC), indicated he's optimistic that Republicans could win the 10 seats they need to retake the majority in the Senate.

"Today we are within striking distance in virtually every race that we need to win if we want to take the Senate," Cornyn wrote in a fundraising e-mail.

Cornyn wrote NRSC supporters to ask for donations after Republicans nominated Ron Johnson in Wisconsin, Kelly Ayotte in New Hampshire and Christine O'Donnell in Delaware as their Senate candidates.

It's the last of those candidates that has outside observers wary of the GOP's chances of retaking the Senate. O'Donnell's upset win in a primary on Tuesday forced projection services like The Cook Political Report to shift their race ratings from predicting a likely GOP pickup to a likely Democratic retention of the seat once held by Vice President Joe Biden.

Republicans, including Cornyn, have rallied around O'Donnell in the wake of her victory over centrist Rep. Mike Castle in the primary, and O'Donnell's campaign on Wednesday said it had raised nearly $1 million. Her campaign had only $20,000 in cash on hand as of late August, according to Federal Election Commission (FEC) filings.

Republicans still face a steep path to victory. Senate Minority Leader Mitch McConnell (R-Ky.) has only said he expects to lead a larger pack of Republicans come next year, though he did predict last week that the GOP would successfully defend all of the seats it currently holds in November's elections.

"These races are close, but they are far from guaranteed victories and the Democrats are going to be sinking millions of dollars to try and save as many liberals as possible," Cornyn wrote of the race. "We are already helping many of our candidates, but we are in desperate need of funds to make sure we can compete in all of these competitive states through the election."