Feingold said he'd constantly heard about instances in other states "that someone wouldn't be appointed because they have a Republican governor in that state or in other words the appointment was just the fluke of who the governor is," said Feingold.
Feingold's plan mirrors what already occurs in the House of Representatives when a seat is vacated, according to Julian Zelizer, a professor of history and public affairs at Princeton University.
"With the House, the Constitution is clear that vacancies have to be filled through special elections, and there is no room to tamper with that," said Zelizer. "But the 17th Amendment, which in 1913 changed to allow the public and not the legislature to vote on a senator, has language in there that basically allows for the appointment process until an election occurs."
"Some say it wasn't meant to be as used as much as it has been," said Zelizer.
Because the problems with the current system have become "very transparent" in recent weeks, Zelizer said he expected Feingold's proposal to gain traction among those who have become fed up with the circus surrounding the latest appointments.
William Keylor, a professor of history at Boston University, agreed with Zelizer, and said the flubbed gubernatorial appointments that have monopolized the front pages will only garner more support for Feingold.
"Public attention is sort of focusing on the inefficiency and the potential for corruption when you allow the governor to simply choose the senator," said Keylor.
Dissent, although how much no one is sure, is almost certain to follow as Feingold holds hearings to address his plan.
"I certainly think there will be resistance," said Feingold. "Governors like their power and will talk to their senators."
Zelizer, too, expects that governors will be the first to react at the possibility that they may have to relinquish some of their power.
"The governors won't be happy," he said. "I'm sure they like this power."
Calls made to the governors in Illinois and Delaware were not immediately returned.
A spokesman for N.Y. Gov. David Paterson told ABCNews.com that the governor has previously spoken about how he views his appointment as an "interim" solution because the public will have its say and vote on the senator in 2010.
But what will likely become more of a sticking point with opponents of the plan will be the logistics of getting a special election organized.
"Some will say it takes more time to get a special election together for a Senate race than it does for a House because it's statewide and the House race is just a district, so theoretically, it will take longer," said Zelizer. "But I don't think that's actually true in this day and age -- if they want to put an election together they could do it."
Keylor added that another drawback of special elections is that turnout is typically much lower than for a regular election, so getting an accurate expression of public sentiment is more difficult. Money is another obstacle that makes gubernatorial appointments seem more attractive to some, said Keylor.
In Illinois, estimates by The Associated Press put the statewide cost of holding a special Senate election at $30 million to $50 million. The state is dealing with a budget deficit of at least $2 billion. New York's next budget, which begins April 1, is projected to have a $12 billion shortfall.
Despite the obstacles, Feingold said he's up to the challenge.
"Constitutional amendments aren't done lightly, but I think this is about perfecting an amendment," said Feingold.
"We have just seen how bad it is to have a governor make this decision. It doesn't fit our democracy."
To amend the Constitution, two-thirds of the Senate and House must first approve and then three-quarters of the states must ratify. It's something that's only been done 27 times in U.S. history.