Blagojevich has been accused of federal corruption, including trying to sell off that seat.
"You know, in all due respect to the Republican National Committee and anybody, right now, I think we should try to be working constructively together, not only on an issue such as this, but on the economy, stimulus package, reforms that are necessary," McCain said in a broadcast interview.
"I don't know all the details of the relationship between President-elect Obama's campaign or his people and the governor of Illinois, but I have some confidence that all the information will come out," McCain said. "It always does, it seems to me."
The Arizona senator said he will disagree sometimes with Obama on important issues, but that the nation's problems are too daunting for political divisiveness.
"I think my job is, of course, to be a part of and hopefully exert some leadership in the loyal opposition. But I emphasize the word 'loyal,'" McCain said.
"Will there be areas of disagreement? Of course. We are different parties and different philosophy," he added. "But the nation wants us to unite and work together."
McCain, who voted against the auto bailout plan rejected by the Senate last week, said he could support an economic stimulus plan proposed by Obama for early next year. But he wants to see the details before committing.
McCain also said it's too early to endorse any of the Republicans who might run for president in 2012, including his former running mate, Alaska Gov. Sarah Palin.
"My corpse is still warm," McCain quipped.
McCain appeared on ABC's "This Week."