"The dollar will stay well-supported until we get some clarification on the tax bill and then we will probably trade off a little bit," said Shaun Osborne, chief FX strategist at Scotiabank in Toronto.
On Monday, the Republican-controlled House of Representatives voted to go to conference with the Senate on tax legislation, setting up formal negotiations on the bill that could take weeks to complete.
The Republican-led Senate is expected to hold a similar conference vote later this week.
In late trading, the dollar index, a gauge of the greenback's value against six major currencies, was up 0.2 percent at 93.329.
Against the yen, the dollar gained 0.2 percent to 112.63 yen . The euro, meanwhile, was down 0.4 percent versus the dollar at $1.1822
Though the dollar has recovered some after falling to a two-month low last week, some market strategists expect further dollar gains next year to be limited.
"Our base case here is that a lot of the good news here is priced into the US dollar," said Scotia's Osborne. "There's not much more upside to the dollar at this point."
ING believes the euro will likely be the beneficiary of any weakness in the dollar.
In a 2018 outlook report on Tuesday, ING strategists said they expect the euro to rise to $1.30 against the dollar next year, a level not seen since September 2014.
"The euro is in the sweet spot of this global recovery and looks well-positioned for the investment cycle," said Petr Krpata, chief EMEA FX strategist at ING in London.
Sterling trimmed early losses to trade down 0.2 percent at $1.3435 as broad disappointment over the lack of a Brexit deal prompted some investors to cut their long bets.
Prime Minister Theresa May failed to clinch a deal on Monday to open talks on post-Brexit free trade with the European Union after a tentative deal with Dublin to keep EU rules in Northern Ireland angered her allies in Belfast.
"I don't think this is a market that is too long sterling, but there definitely has been an increase in the excitement level of late with sterling/dollar staying very close to a nice uptrend over the last several months," said W. Brad Bechtel, managing director at Jefferies LLC in New York.