Sen. John McCainJohn Sidney McCainGOP strategist donates to Alabama Democrat Meghan McCain knocks Bannon: 'Who the hell are you' to criticize Romney? Dems demand Tillerson end State hiring freeze, consult with Congress MORE (R-Ariz.), one of the president’s fiercest critics, says President Obama shouldn’t be impeached.

On Fox Business Network's “Imus in the Morning” Thursday, McCain was asked to react to Sarah Palin’s call this week for Obama to be impeached.

“Well, I don't agree and I remember going through an impeachment of William Jefferson Clinton,” he said. “There are not votes here in the United States Senate to impeach the president of the United States and I think that we should focus our attention on winning elections.

"We win this election and regain control of the United States Senate, we can be far more effective than an effort to impeach the president, which has no chance of succeeding.”

Host Don Imus pressed McCain even further and asked whether he would support impeaching him if it could succeed.

“No, but I mean, that's just not in the realm of reality,” he said, adding that it would require 67 votes in the Senate.

McCain was pressed further and still stood by his position, though he said he agrees with critics who say Obama has overstepped his bounds.

“My answer is no, I think that by enacting a series of reforms, legislation, working with our colleagues in the house, we could have a far greater effect. But there's no doubt in my mind that the president has abused his constitutional authority as president of the United States.” 

Palin, McCain's running mate in the 2008 presidential election, called for Obama to impeached over the border crisis on Tuesday, sparking a fresh debate among conservatives.

Speaker John Boehner (R-Ohio) shot down calls for Obama’s impeachment on Wednesday, as did other hard-right Republicans.

On "Imus," McCain criticized Obama for his remarks from Texas Wednesday regarding the humanitarian crisis on the U.S. border. The Republican said he’s dealt with five other presidents, both Republicans and Democrats, who would have expressed a conciliatory strategy toward Congress.

“Instead he just chose to beat up on the Congress, and I don't think that's productive, to be honest with you,” said McCain.

Obama outlined the administration’s planned response to the influx of unaccompanied children if Congress approves the $3.7 billion package sent to Capitol Hill earlier this week. He also summarized a meeting he had with Texas Gov. Rick Perry about possible solutions to the crisis.

McCain was among a number of lawmakers — including some Democrats — who urged Obama to visit the border on his visit Wednesday. He said he should have at least paid border patrol a visit to thank them.

“Wouldn't it be appropriate for the president to have at least stopped by and thank them for the hard work they're doing?”