* C$ at C$1.0303 vs US$, or 97.06 U.S. cents * GDP picks up in July; investors wary of U.S. budget battle * Bond prices rise across the curve By Leah Schnurr TORONTO, Sept 30 (Reuters) - The Canadian dollar was unchanged on Monday, giving back earlier gains on better-than-expected economic growth as investors focused on events south of the border where the clock was ticking to avoid a U.S. federal government shutdown. The Canadian economy grew by 0.6 percent in July, rebounding from a contraction the previous month when the recovery was hurt by flooding in Alberta and a construction worker strike in Quebec. Even with the improvement, the economy remains well below the central bank's estimate of the potential growth in output. "Basically, this was just a mirror image of the June decline," said Doug Porter, chief economist at BMO Capital Markets in Toronto. "The broader story is when we look past those two volatile months, the economy is still just grinding ahead at a relatively sluggish pace." The Canadian dollar ended the session at C$1.0303, or 97.06 U.S. cents, unchanged from Friday's close. The loonie earlier traded as high as C$1.0275, marking its strongest level in nearly a week. But investors shied away from taking aggressive bets as the possibility of a federal government shutdown in the United States drew closer. If a stop-gap spending bill for the new fiscal year is not passed before midnight on Monday, government agencies and programs deemed non-essential will begin closing their doors for the first time in 17 years. Investors are concerned about the impact such a shutdown would have on the still-fragile U.S. economic recovery. The uncertainty pushed the greenback down 0.1 percent against a basket of currencies. While the markets may be able to shrug off a shutdown that lasts only a couple of days, investors are unlikely to be able to withstand something longer, said Don Mikolich, executive director of foreign exchange sales at CIBC World Markets. "Because of the economic linkages, any kind of slowdown in the U.S. as a result of the government shutdown would eventually feed through to be negative for Canada," he said. The political battle also increased concerns about lawmakers' ability to reach a deal to raise the debt ceiling by mid-October. Failure to do so could cause the United States to default on some payment obligations. Prices for Canadian government bonds were higher across the maturity curve. The two-year bond was up 2.2 Canadian cents to yield 1.190 percent and the benchmark 10-year bond rose 15 Canadian cents to yield 2.541 percent.