FLC OF MLG MADE MAP AT DCA FROM THE LDA DME APCH. NORMAL LNDG ON SECOND APCH.

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WE WERE VECTORED TO INTERCEPT THE LDA AND WHEN CLRED FOR THE APCH; VOR LOC WAS ENGAGED WITH THE FLT DIRECTOR PROVIDING LDA GUIDANCE. THE GS WAS FOLLOWED; WITH THE STEP DOWN ALTS AS BACK UP; DOWN TO THE 720 FT MDA; WHICH WAS REACHED AT APPROX 2.9 LDA DME. SINCE THE RWY WOULD BE VISIBLE ON THE R SIDE OF THE AIRPLANE; AND SINCE I WAS THE PF; THE FO MADE THE VISUAL SEARCH FOR THE RWY AS SOON AS WE BROKE OUT OF THE OVCST WHICH WAS ALMOST SIMULTANEOUSLY TO REACHING MDA. JUST BEFORE INTERCEPTING THE EXTENDED CENTERLINE OF RWY 18; AT APPROX 1.8 LDA DME; THE FO ANNOUNCED RWY IN SIGHT. I VISUALLY CONFIRMED RWY 18 IN SIGHT; BANKED R; AND BEGAN A DSCNT FROM MDA. ONCE WE WERE LINED UP WITH RWY 18; IT BECAME EVIDENT THAT WE WERE TOO HIGH TO MAKE A NORMAL DSCNT TO LNDG. DCA TWR ASKED IF WE WOULD BE ABLE TO GET DOWN. WE RESPONDED THAT IT WOULD NOT BE POSSIBLE AND WE WOULD BE EXECUTING A MISSED APCH. WE WERE INSTRUCTED TO CLB TO 2000 FT; THEN TO TURN L HDG 090; THEN TO CLB TO 3000 FT. WE WERE THEN VECTORED FOR A SECOND LDA DME 18 APCH. THIS TIME THE RWY CAME INTO VIEW ABOUT A MI SOONER AND WE WERE ABLE TO DSND ON A NORMAL GLIDEPATH TO RWY 18 FOR NORMAL LNDG.