"There is the possibility for some further volatility on the U.S. budget/debt ceiling issues, but I think the market is still largely anticipating a benign outcome," said Todd Elmer, head of G10 foreign-exchange strategy for Asia excluding Japan at Citigroup in Singapore. "This is why I would look for only downward drift in USD in anticipation of some resolution before the debt ceiling is hit. I would look for 1-2 percent further drop from the dollar."
The vast majority of respondents in CNBC's latest poll of currency market sentiment (96 percent, or 23 out of 24 respondents) believe the U.S. dollar will continue to slide. A single respondent is 'neutral' and expects prices to trade around current levels. None of the strategists and analysts polled expects the dollar to gain.
The dollar index rebounded on Friday from Thursday's eight-month low of 79.627. The index lost 0.17 percent on the week, its fourth straight week with a loss.
"I expect further dollar weakness but no more than a 1 percent sell-off in DXY because I expect a resolution to the fiscal showdown soon," said Kathy Lien, managing director of FX Strategy for BK Asset Management. "I'm mildly bearish USD week ahead. I'm expecting no more than a 1 percent deviation in all pairs in the coming week."
(Read more: Dollar shorts get louder as shutdown continues)
Khoon Goh, senior FX strategist at ANZ, said the dollar index may breach key support at around 79 next week while the euro could test the year's high of $1.37 which may position the currency for a move towards $1.38. Sterling is eying a move to $1.63, Goh said, which would imply a break of the 9-month high of $1.6260 hit on October 1. "In all, bearish for USD. But it could all turn quickly if the Democrats and Republicans manage to do a deal," he said.
Consensus opinion amongst most of the strategists polled is focusing on a drop in the dollar index towards 79.00. Westpac's Sean Callow said he's targeting levels of around 79.25/30 while Ed Ponsi of Barchetta Capital said the index is heading to 79.00.
"Conventional wisdom would favor dollar strength in the face of a GDP-sapping shutdown (flight to safety), but the technicals predicted dollar weakness via a bear flag," Ponsi said. "This round goes to the technicals."
Technical analysts agreed that dollar continues to look vulnerable. Louise Yamada, Managing Director of Louise Yamada Technical Research Advisors, LLC said the dollar index may fall to 79-78 in the short term.
The U.S. dollar's continued weakness may be most accentuated against the Japanese yen, strategists noted, and some warned of a dip in the cross below 96.00.
(Read more: Debt ceiling? The dollar doesn't care)
"USDJPY...is showing signs of wanting to break lower, squeezing what is the main position in the G10 market," said Sebastien Galy, senior currency strategist at Societe General. "We would target 96.0 and maybe a bit lower as key supports are broken."
Galy added: "However, this is all very tactical trading. The real deal is to buy it when the market panics as Abenomics is in no way gone and fair value is around 99. Eventually, in the many months ahead, widening interest rate differentials will lead the JPY lower."
—By CNBC's Sri Jegarajah. Follow him on Twitter