But it is unclear whether any of their ideas is likely to be imposed on a country that has nuclear weapons and whose cooperation is seen as vital to stabilizing Afghanistan as the United States prepares to pull out from there by the end of 2014.
Former Massachusetts Governor Mitt Romney said Pakistan has multiple centers of power including the relatively weak civilian leadership, the military and the powerful intelligence agency know as the Inter-Services Intelligence Directorate.
"The right way to deal with Pakistan is to recognize that Pakistan is not a country, like other countries, with a strong political center that you can go to and say, 'Gee, can we come here, will you take care of this problem?'" Romney said.
"This is instead a nation which is close to being a failed state. I hope it doesn't reach that point, but it's really a fragile nation," he said.
Polls point to Romney as the Republican who would be the most likely among the party's crop of candidates to defeat President Barack Obama, a Democrat, in the November 2012 U.S. presidential election. The Republicans begin choosing their nominee in state contests beginning in January.
Texas Governor Rick Perry suggested that every country, including Pakistan, should see its U.S. aid eliminated each year and then should convince the United States why it deserves any money at all.
"Then we'll have a conversation in this country about whether or not a penny of our taxpayer dollars needs to go into those countries," Perry said in response to a question about whether Islamabad was playing a double game with Washington.
"Pakistan is clearly sending us messages ... that they don't deserve our foreign aid ... because they're not being honest with us," he added.
"American soldiers' lives are being put at jeopardy because of that country ... and it's time for us as a country to say no to foreign aid to countries that don't support the United States of America," he said.
Businessman Herman Cain had difficulty offering a direct response when asked whether Pakistan was ultimately an ally or adversary. "There isn't a clear answer as to whether or not Pakistan is a friend or foe," Cain said."
U.S. officials have long argued that the Taliban and other militants enjoy safe havens in Pakistan from which they attack U.S. soldiers in neighboring Afghanistan.
They privately argue Pakistan plays a double game, taking billions of dollars in U.S. aid while elements of its government tolerate militant groups such as the Haqqani network blamed for a September attack on the U.S. embassy in Kabul.
Pakistan says it has made more sacrifices than any other country in the war against militancy, losing about 10,000 members of its military and security forces.
There have been growing questions in Washington about whether U.S. troops should to go after Taliban safe havens in Pakistan, an idea sure to be deeply unpopular in a population already embittered by U.S. drone strikes.
Some Republican candidates argued that the United States has little choice but to nurture relations with Pakistan, citing the fact that it has nuclear arms and that it has to be part of the solution in Afghanistan.
"Pakistan must be a friend of the United States for the reason that Michele (Bachmann) outlined. Pakistan is a nuclear power," said former Pennsylvania Senator Rick Santorum, referring to fellow Republican candidate Bachmann.
"It's important for us, with a nuclear power with a very vast number of people in Pakistan who are radicalizing, that we keep a solid and stable relationship and work through our difficulties," he added.
