* TSX up 1.3 pct, or 164.08 points, to 12,894.41 * Potential for break in U.S. impasse boosts equities * Canadian Natural Resources up more than 4 pct By Leah Schnurr TORONTO, Oct 10 (Reuters) - The main Canadian stock index racked up its best day in three months on Thursday as investors were encouraged by signs U.S. lawmakers were making progress in negotiations to raise the debt ceiling. U.S. politicians are locked in a budget stalemate that has resulted in a partial government shutdown now in its tenth day. The impasse is bringing lawmakers closer to a separate mid-October deadline to raise the debt ceiling to avoid a potential default that would roil world markets. Republicans in the House of Representatives on Thursday put forward a plan that would delay that deadline by roughly six weeks, giving the government, and markets, some breathing room. "The debt issue was a very good excuse to stay on the sidelines, but now that there's some hope that the situation will be resolved, we're seeing people get back into the market in a hurry," said Elvis Picardo, strategist and vice president of research at Global Securities in Vancouver. "You're now down to the final quarter of the year, so there's a ton of money that needs to be put to work." The Toronto Stock Exchange's S&P/TSX composite index jumped 1.3 percent, or 164.08 points, to 12,894.41. It was the biggest increase since early July, though it lagged the equities rally south of the border where the three major indexes climbed more than 2 percent. Canadian Natural Resources was one of the biggest boosts of the day after the oil explorer and producer reported stronger-than-expected cash flow. The stock climbed 4.5 percent at C$33.46. Shares of BlackBerry rose 0.6 percent to C$8.49 after co-founder Mike Lazaridis increased his stake and was considering buying the entire company. Three banks were among the top five performers, with Royal Bank of Canada up 1.9 percent at C$67.69, Toronto-Dominion Bank gaining 1.3 percent at C$92.30, and Bank of Nova Scotia adding 1.3 percent to C$59.72.