As far as increasing the size of the House goes, the size of the House was fixed at 435 by the Reapportionment Act of 1929. Congress has the authority to alter the size of the House whenever it wishes by passing a new law. The Constitution's only input on the matter is that a Representative may have no less than 30,000 people in their district.
Since the 1790 Census, Congress had varied the size of the House of Representatives after each census. Often there were considerations such as preventing a slow-growing state from losing representation. There were also debate about the method of apportionment.
After the 1910 Census, the size of the House of Representatives was set at 433, with the anticipation that the admission of Arizona and New Mexico to the Union would increase it to 435 (I think Arizona and New Mexico were actually conditionally incorporated in the reapportionment bill).
After the 1920 Census, Congress failed to reapportion. The 1910's had seen a sever drought in the Midwest that had seen farm state population remain static after having increased every census. Meanwhile states in the Northeast and Great Lakes area were seeing large growth in cities due to industrialization. So New York would gain bunches of representatives, while midwestern states would lose.
Finally, President Hoover pushed through reapportionment legislation that defined the method of apportionment and set the size of the HoR at 435, with the apportionment formula applied automatically. This was used in 1930, and basically there has never been an impetus to change it since. At best, you might have congressmen from states losing representation filing a bill to increase the size of the HoR.
When Alaska and Hawaii were admitted to the Union in 1959 and 1960, they were apportioned a single representative each, increasing the size of the HoR to 437, and the number of electors from 531 to 537. The law also provided that the HoR would revert to 435 representatives after the 1960 Census, which it did. Since Hawaii gained a 2nd representative as a result of the census, other states in effect lost 3 representatives.
Because of the passage of the 23rd Amendment (DC Presidential Vote), the number of electors changed from 537 in 1960 to 538 in 1964.
The current legislation, provides that the 2 additional representatives due not increase the size of the HoR on a permanent basis (it will revert to 435 after the 2010 Census). It addition, it states that Utah will not gain an (6th) elector for the 2008 presidential election.
It appears that after 2010 Census that the number of electors will decrease to 537 (since DC will have one of the 435 representatives), but its number of electors is based on the 23rd Amendment and not on its number of House Members.