The Rangers 40 man roster is full, so two moves will have to be made to make room for Rhodes and Webb.
Wilmer Font is out for the season with Tommy John surgery, and thus would be a candidate for the 60 day d.l., but I don't think he can be placed on the 60 day d.l. just yet...I'm not sure, but I think you can't do that until sometime in March.
Other potential DFA candidates are Max Ramirez, who is out of options, 4th on the catching depth chart, and struggling to regain his offensive value; Pedro Strop, who has great stuff but hasn't been able to convert that to results at the major league level; Guillermo Moscoso, who has good stuff but hasn't been able to convert that to results at the major league level; Clay Rapada, a lefty specialist on a team with quite a few lefty options; and Rule 5 pick Mason Tobin.
I've been wondering if the Rangers were delaying the announcement because of a potential trade that would clear a 40 man roster spot or two, and it is possible that one or more of those guys above have already been run through waivers and cleared.
But in any case, there's going to be a couple of roster casualties shortly, plus a third player removed when the Rangers end up signing either Adrian Beltre or a DH.