American Stricker, widely regarded as one of the game's best putters, said he had changed his view after consistently opposing the use of long putters and that he would not be surprised to see the tour dig in its heels.
Fellow veteran Furyk, like Stricker a member of the tour's policy board, disagreed with the proposed ban while he supported 'bifurcation' whereby professionals and amateurs could play under different rules.
"It's kind of confusing," Stricker told reporters while preparing for Wednesday's opening round of the WGC-Accenture Match Play Championship at Dove Mountain.
"I'm really not for the long putter, but I'm really not for the change, either. The timing is bad. We're at a point in time when we really don't need to be messing around with it.
"I don't know if that's going to happen, don't even know if the USGA is going to go ahead with the rule change. But I can see the (US PGA) Tour adopting the rule saying that it's okay for players to use a long putter."
In November, the game's governing bodies proposed a ban on players anchoring putters to their body, saying they wanted to outlaw the practice by 2016 in order to preserve the "skill and challenge" of putting.
Players and the golfing community were then given 90 days in which to discuss that proposal by the Royal and Ancient (R&A) and United States Golf Association (USGA), a period which concludes at the end of this month.
The announcement by the rulemakers came after three of the past five Major champions had used 'belly' putters - Keegan Bradley (2011 US PGA Championship), Webb Simpson (2012 US Open) and Ernie Els (2012 Open).
US PGA Tour Commissioner Tim Finchem discussed the proposed ban on a conference call with his 16-member player advisory council on Monday, and afterwards with the tour's policy board.
"Our game out here on tour is pretty strong," said Stricker, a 12-times winner on the US circuit. "There are a few players that have won Majors with a long putter, and they're faces of our tour.
"And to take that away, I think, is not a good thing for our tour or our sport at this time."
Furyk, who won his only Major title at the 2003 US Open, told Golf Week magazine he was opposed to any change given that long putters had been in use for the last 40 years.
"I disagree with the rule," Furyk said. "I think it's just been too long. But I wouldn't want to do something differently from the USGA, as well, because that opens a whole new can of worms in the world of golf.
"Every sport that I can think of has different sets of rules for different abilities and different styles, and I realize that's not what the USGA wants to do. I just really don't understand why."
Former world number one Tiger Woods has been another long-term opponent of the belly putter but he expressed a more balanced view on Tuesday.
"Well, I understand if we go either way," he said. "We put in local rules every week, and this may or may not be a local rule. But we'll see what happens."
The R&A and USGA say putters should swing freely and not be anchored to any part of the body, and that swinging a club freely has been the essence of the 600-year-old sport.
The proposed new rule would come into force on January 1, 2016.
"This timetable would also provide an extended period in which golfers may, if necessary, adapt their method of stroke to the requirements of the rule," the R&A said in November.