I'm uncertain what is meant by a "default warrant". My suspicion is that it was warrant issued by a judge for the Defendant's failure to appear in court as required. If that is correct, it is the equivalent of any other arrest warrant for an individual. Such a warrant provides authority to enter and search for the Defendant in his residence residence. That warrant does not supply authority to conduct a general search of the premises or to continue a search after the Defendant has been located and taken into custody. Hopefully the Defendant has a good criminal defense attorney.
In a word: yes. As Attorney Jones points out above, there are limits on the scope of a default warrant. But failure to appear in court can lead to a default warrant issuing for your arrest.
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There are two issues here: whether they can arrest you on a warrant (default warrant simply means you "defaulted" or did not show for a scheduled court appearance, and therefore were subject to being arrested) and whether they can search your house as part of that arrest.
The first part is whether they can enter your home and arrest you on a warrant, and the answer is "yes."
The second part is whether they can search the place in the process, and the answer is "no," not without a search warrant. Your characterization as "forcing" their way in leaves a lot of detail that is subject to interpretation. You should definitely speak with a criminal defense attorney as soon as possible to preserve and collect evidence to support your position.
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