* Front month above last week's 10-year spot chart low * Mild weather on tap long-term for much of the nation * U.S. crude futures rise in early trade * Coming Up: API oil data Tuesday, EIA oil data Wednesday By Eileen Houlihan NEW YORK, April 24 (Reuters) - U.S. natural gas futures seesawed on either side of positive territory early Tuesday, hovering near the key $2 per million British thermal unit level and remaining above last week's 10-year spot chart low. While some traders said a 9 percent drop in the first half of April left the market oversold and due for a bounce, most expect little upside near-term, with mild spring weather on the horizon and record supplies adding weight to the downside. Front-month May natural gas futures on the New York Mercantile Exchange, which expire on Thursday, were at $2.00 per mmBtu in early trade, down 0.7 cent, after sliding twice last week to $1.902, its cheapest price since January 2002. HUGE INVENTORY SURPLUS STILL WEIGHS U.S. Energy Information Administration last week showed total gas inventories rose to 2.512 trillion cubic feet, remaining at record highs for this time of year and standing 53 percent above last year and about 58 percent above the 5-year average level. (Storage graphic: link.reuters.com/mup44s) Early injection estimates for this week's EIA storage report range from 35 bcf to 70 bcf versus a year-ago gain of 35 bcf and a five-year average build of about 47 bcf for that week. If weekly stock builds through October match the five-year average pace, inventories would top out at 4.594 tcf, or about 11 percent above peak estimated capacity of about 4.1 tcf. That could sink prices later in the injection season if storage caverns fill up and force more gas into a well-supplied market. PRODUCTION ALSO NEAR RECORD HIGHS The EIA's short-term energy outlook this month also offered little hope for bulls, with the agency sharply raising its estimate for marketed gas production this year for a third straight month. Production growth is expected to slow this year as low prices hit plans for new drilling, but the sharp decline in the Baker Hughes gas rig count -- down a third since peaking at 936 in October -- has not yet reduced output partly due to increased drilling efficiency. The gas-directed rig count rose last week for only the third time this year, up 7 from the previous week's 10-year low. (Rig graphic: r.reuters.com/dyb62s) MORE FUNDAMENTALS The National Weather Service's six- to 10-day outlook issued on Monday called for above-normal readings for about the eastern two-thirds of the nation, with normal readings only in the West. Spring nuclear power plant outages were running at about 25,100 megawatts, or 25 percent, on Tuesday, down from about 29,800 MW out a year ago but above the five-year outage rate of about 22,700 MW. (Reporting by Eileen Houlihan;editing by Sofina Mirza-Reid)

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