* Investors look past Obama re-election, focus on 'fiscal cliff' * ECB's Draghi: euro zone to remain weak in the near term * Greece, Spain worries dent euro sentiment By Wanfeng Zhou NEW YORK, Nov 7 (Reuters) - The dollar rose to a two-month high against major currencies on Wednesday as investors shifted focus to U.S. fiscal woes after President Barack Obama's re-election, bolstering the appeal of the safe-haven U.S. currency. The euro came under pressure after European Central Bank President Mario Draghi said the bank expects the euro zone economy to remain weak "in the near term," adding to investor nervousness ahead of the central bank's policy meeting on Thursday. The U.S. president faces a fresh challenge confronting the "fiscal cliff," a mix of tax increases and spending cuts due to extract some $600 billion from the economy starting Jan. 1 barring a deal with Congress. "Key macroeconomic and event risks persist, including the ability of U.S. policy-makers to effectively address the looming U.S. 'fiscal cliff' and the unrelenting negative news flow emanating from the euro zone's sovereign debt crisis," said Samarjit Shankar, managing director of global FX strategy at BNY Mellon in Boston. "These may prove to be supportive of the greenback as investors stay cautious." The dollar index, which tracks the greenback versus a basket of currencies, rose 0.22 percent to 80.792, having hit as high as 80.924, its highest since Sept. 7. In the past several years, the dollar has tended to benefit from bad news about the global economy, even when the worries stem from the United States, because investors see the U.S. Treasury market as a safe haven. "And while there's evidence that relation has moderated, it's still there," said Ron Leven, senior currency strategist at Morgan Stanley in New York. The euro fell as low as $1.2734 on Reuters data, a two-month low, hurt by grim economic forecasts for the euro zone and continued sovereign debt-related worries in Greece and Spain. It was last at $1.2761, down 0.4 percent. Against the yen, it lost 1 percent to 101.91 yen. The currency faced further pressure ahead of a Greek parliamentary vote on austerity measures necessary to secure the next tranche of bailout cash, without which the country faces bankruptcy. "If the Greek vote doesn't go through, there is a lot of downside risk to the euro as talk of a Greece exit will re-emerge," said Jane Foley, senior currency strategist at Rabobank. Prime Minister Antonis Samaras is expected to narrowly win but the smallest party in his coalition will oppose the measures, leaving him with a margin of just a handful of votes. The market also remained concerned that Spain could delay seeking international aid. The European Central Bank will decide on interest rates on Thursday and while no change is expected, a slew of grim data out of the euro zone is likely to keep alive chances of further cuts. Earlier in the day, the clear-cut U.S. election result had lifted stocks and riskier currencies. The higher-yielding Australian dollar rose to its best level in nearly seven weeks against the greenback and the Canadian dollar hit a three-week peak. But that trend soon fizzled out as investors turned their attention to the euro zone's problems and the U.S. fiscal cliff. Some analysts said strength in the dollar could be limited as Obama's win means the Federal Reserve's monetary policy is likely to remain accommodative. Against the yen, the dollar fell to as low as 79.76 yen on Reuters data, well below its six-month high of 80.67 hit last week. It was last down 0.6 percent at 79.86 as yields on U.S. Treasuries fell sharply. Analysts at Morgan Stanley said they are maintaining their bullish strategy for dollar/yen and expected a re-test of the 80.70 high, with a break above there opening the way for gains towards their 84.00 target.