Sea Level:
First, what is supposed to be causing it? Melting of ice due to warming. Let's grant for a moment that this is happening at a rate fast enough to be serious. The question still remains what is causing the warming? For example, could it be solar influences? See e.g.
Camp, C. D., & Tunk, Kk. (2007). Surface warming by the solar cycle as revealed by the composite mean difference projection. Geophysical research Letters 34.
Douglass, DH, Clader, DB, & Knox, RS. (2004). Climate sensitivity to Earth to solar irradiance: update. Paper presented at 2004 Solar Radiation and Climate (SORCE) meeting on Decade Variability in the Sun and the Climate, Meredith, New Hampshire, October 27-29, 2004
Harrison, R. G., & Sephenson, D. B. (2006). Empirical evidence for a nonlinear effect of galactic cosmic rays on clouds. Proceedings of the Royal Society London, Ser. A, 462, 1221-1233.
Kirkby, J. (2008). Cosmic rays and climate. Surveys in Geophysics 28 pp. 222-275.
Scarfetta, N., West B. (2007). Phenomenological reconstructions of the solar signature in the northern hemisphere surface temperature records since 1600. Journal of Geophysical Research 112.
Shaviv, N J. (2005) On climate response to changes in the cosmic ray flux and radiative budget. Journal of Geophysical Research 110.
Svensmark, H. (2007). Cosmoclimatology: A new theory emerges. Astronomy & Geophysics 48.
Svensmark H. et al (2007). Experimental evidence for the role of ions in particle nucleation under atmospheric conditions. Proc. Roy. Soc. A 463 385-396
Tinsley, B. A. & Yu, F. Atmospheric Ionization and Clouds as Links Between Solar Activityand Climate. American Geophysical Union monograph, 141, 321-340.
Usoskin, I. G. et al (2003). Millenium-scale sunspot number reconstruction: Evidence for an unusually active sun since the 1940s. Physical Review Letters 91.21
Viezer, Jan. (2005). Celestial Climate Driver: A perspective from four billion years of the carbon cycle. Geoscience Canada 32.
And, of course, in order for GHGs to be the cause of melting, the there need to be positive feedbacks, but is this the case? See e.g.
Compo, G. & Sardeshmukh, P.D. (2008). Oceanic Influences on Recent Continental Warming. Climate Diagnostics Center, Cooperative Institute for Research in Environmental Sciences, University of Colorado, and Physical Sciences Division, Earth Sytem Research Laboratory, National Oceanic and Atmospheric Administration, Boulder, Co.
Kininmonth, W. (2004). Climate Change: a natural hazard. Multi-Science Publishing, Brenwood.
Koutsoyiannis, D. et al. (2008). On the credibility of climate predictions. Hydrological Sciences/Journal des Sciences Hydrologiques, 53 (4), 671-684.
Lindzen, et al. (2001). Does the earth have an adaptive infrared iris? Bulletin of the American Meteorological Society 82, 417-432.
On the problems with surface records, see in particular:
De Laat, A.T.J., & Maurellis, A.N. (2006). Evidence for influence of anthropogenic surface processes on lower tropospheric and surface temperature trends. International Journal of Climatology 26
McKitrick, R.R., & Michaels, P. J. (2007). Quantifying the influence of anthropogenic surface processes and inhomogenities on gridded global climate data. Journal of Geophysical Research 112.
But let's turn specifically to the issue of melting ice. How about the largest mass of ice on the planet? Antarctica? First, it has been melting over the last 6000 years. However, it seems that the rate of melting is either decreasing or that the ice has actually increased over the past 30 years. See, e.g.:
Liu, J., Curry, J. A., & Martinson, D. G. (2004). Interpretation of recent Antarctic sea ice variability. Geophysical Research Letters 31
Vyas, N. K., Dash, M. K., Bhandari, S. M., Khare, N., Mitra, A., and Pandey, P. C. (2003). On the secular trends in sea ice extent oer the antarctic region based on OCEANSAT-1 MSMR observations. International Journal of Remote Sensing 24.
Parkinson, C. L. (2002). Trends in the length of the southern Ocean sea-ice season, 1979-99. Annals of Glaciology 34.
Of course, much of the focus on glacial melting has centered on the arctic. But even the IPCC admits (2007, p. 252), “a few areas have cooled since 1901.”
Also, the other problem is that the period of recent warming comes right after a period of cooling, during which arctic ice increased, and before that, ice decreased due to a period of warming which had nothing to do with AGW. In fact, this period of warming may be causally related to the current melting (see e.g. Professor Mahoney’s seminar given in 2007 at the University of Colorado). Also, the warming in the arctic may have nothing to do with AGW. See e.g. Semenov, V. A., & Bengtsson, L. (2003). Modes of the Wintertime Arctic Air Temperature Variability. Geophysical Research Letters 30.
Perhaps most importantly, though, is the history of melting in the past, even the recent past. Dahl-Jensen et al (1998) note that both the Holocene Climate Optimum and Medieval Warming period were warmer in Greenland than today. As for how fast or rapid warming can occur naturally, see e.g. Bard, E. 2002. Climate shock: Abrupt changes over millennial time scales. Physics Today 55(12).
In Greenland, there is evidence for cooling and again an increase in the amount of ice. See, e.g., Hanna, E. & Cappelen, J. (2002). Recent climate of Southern Greenland. Weather 57 as well as Hanna, E. and Cappelen, J. (2003). Recent cooling in coastal southern Greenland and relation with the North Atlantic Oscillation. Geophysical Research Letters 30.
The point is, glaciers everywhere advance and retreat all the time (see e.g. Braithwaite, R. L. (2002). Glacier mass balance: The first 50 years of international monitoring. Progress in Physical Geography 26.